Shamrock Rovers' hopes of causing a major shock in the Europa League were dashed as they were beaten 2-0 by an impressive AC Milan side at Tallaght Stadium. 

A goal in either half proved enough for the Italian giants who dominated the Dublin side for large parts of this entertaining encounter. 

Swedish superstar Zlatan Ibrahimovic opened the scoring with a fine finish in the 23rd minute before the stylish Hakan Çalhanoğlu secured safe passage through to the next round for the Rossoneri with a well-hit effort in the 67th minute. 

The home side enjoyed plenty of chances to get back into the game but were held scoreless thanks to a string of fine saves from Milan keeper Gianluigi Donnarumma. 

A bright start at the stadium by the visitors who, as expected, gained control of the ball early on and worked the play nicely into the Hoops half. An early look at goal from Alexis Saelemaekers was sliced well wide in the second minute before a dangerous corner a minute later flew across the face but there was no Milan man on hand to cause concern. 

Understandably, Rovers looked cautious and a touch nervous on the ball but had a moment going forward when Ronan Finn’s pace put pressure on Theo Hernandez; who was forced back to his keeper. 

Again, though, Milan pushed forward and caused a bit of panic in the home defence with Lee Grace slamming the ball back at his own keeper to allow the pressure to build. 

Ten minutes in and the Hoops were still intact and trying to grow into the game, but Milan worked a decent chance to the back post from a set-piece. Ibrahimovic was unmarked but could not direct his header on target and he really should have left it for the arriving Saelemaekers who would have had a great chance to open the scoring. 

The best chance of the game came in the 14th minute and it was Rovers who worked Milan keeper Donnarumma, who had to get down sharply to palm away a stinging Aaron Greene effort. 

Jack Byrne was the creator as he strode with confidence through the heart of the Milan midfield before rolling his striker through on the left of the goal – the first-time effort a real wake-up call for the esteemed visitors. 

Milan resumed with their calm, controlled passing, working the ball into the final third, yet without threatening. Rovers defended in numbers and while the composure was again lacking, the commitment to the cause ensured that no clear-cut openings presented themselves. 

The deadlock, however, was broken in the 23rd minute as Ibrahimovic slammed the ball home from about 12 yards out. 

Rovers were boxed in on the right flank and while they tried to pass their way out of trouble through Finn and Joey O’Brien, the ball finally pinged at Lopes and the defender’s clearance was intercepted by Hernandez, which led to a quick ball played inside to the big Swede who had time to work a one-two with Çalhanoğlu. 

The result never in doubt as Ibrahimovic pulled the trigger from close range to beat Alan Mannus at the keeper’s near post. 

Milan almost doubled the lead two minutes later as a quick counter sent Ibrahimovic down the left. Goalscorer turned provider as he sent a delightful ball right across the face, on a plate for the arriving Samu Castillejo. 

Mannus flung himself forward at the feet of the arriving forward but a perfect shot was flying into the back of the net only for the ever-alert Arron McEneff to somehow get his body between ball and goal and clear the danger. 

Rovers fought their way back into it and created two chances inside two minutes following some good work up the right by Joey O’Brien, who eventually worked the ball forward towards Greene. 

The striker stayed strong to bundle Matteo Gabbia out of the way before drilling another shot on target, this time to the keeper’s left post, but again the Milan skipper was up to the task. 

From the resulting corner, Lopes made a trademark front-post run but his glancing header flew over the bar without threatening. 

Milan enjoyed more ball in the Rovers area and had two shots at goal within two minutes but neither Hernandez nor Turkey international Çalhanoğlu could work Mannus. 

Another chance for Ibrahimovic with three minutes remaining in the first half but this time his curling effort was lifted over the bar. 

It came as a result of yet another defensive block in front of goal, with Lopes throwing his body in front of Davide Calabria’s stinging effort. 

The Hoops had a chance to restore parity a minute before the break as a great move saw Stephen Bradley’s side work the ball all the way up the left flank before Neil Farrugia found space to lift the ball to the back post. 

Finn arrived unmarked and had time to direct his header goalwards, unfortunately for the Dublin side, the midfielder’s effort was tame and resulted in a standard save. 

It took seven minutes for the second half to warm up, as Çalhanoğlu’s speculative effort glanced the crossbar following a looping overhead kick. The ball was only cleared to the edge of the box for the arriving Davide Calabria whose goalbound effort was well stopped by Mannus high up at his near post. 

The Italians maintained the pressure as they sensed they could perhaps kill this game off with a second goal, however, they were trying to walk the ball into the back of the net, attempting intricate passes inside the box without threatening the goal. 

Ibrahimovic was then taken down on the edge of the box with 58 minutes on the clock. 

Çalhanoğlu whipped the ball in from a tight angle and it looked to be heading inside the far post only for the fingertips of the Hoops keeper. 

Rovers found themselves under serious pressure midway through the half as it looked as though they were trying to contain the visitors and stay in the game into the latter stages. 

But no matter how hard the Rovers defence and midfield unit tried to play their way out and up the pitch, they were stopped in their tracks with the Italian side really starting to turn the screw. 

And there was no surprise when the net eventually rippled in the 67th minute as Çalhanoğlu found space on the edge of the box before drilling an unstoppable shot past Mannus who could do little as it flew into the right corner of the net. 

Rovers had no option now but to go for it and Dylan Watts was sent on to replace holding midfielder Gary O’Neill, and the substitute made an immediate impression as he cut down the right flank before pulling a dangerous ball across the face of the goal. 

Greene was again on hand to work the ball on target and again Donnarumma was forced to make a fine save to maintain the two-goal lead. 

Milan finally took a breather with 15 minutes remaining on the clock and with firm control over this one-leg tie. 

A plethora of changes killed the tempo as Milan worked their way down through the gears, while Rovers had little left to give in the energy department. 

Watts did manage a shot on target for the Hoops as the game moved into injury time, but the deflected effort was easy enough for the keeper who did not put a foot wrong all night. 

So the League of Ireland title contenders bow out after a brave and battling performance and they will turn their attention back to securing league honours next week with a home clash against Waterford on Monday. 

Shamrock Rovers: Alan Mannus; Roberto Lopes, Joey O’Brien, Lee Grace; Neil Farrugia (Sean Kavanagh 83), Ronan Finn, Gary O’Neill (Dylan Watts 70), Aaron McEneff, Jack Byrne; Graham Burke, Aaron Greene (Dean William 88) 

AC Milan: 99 Gianluigi Donnarumma (captain); 2 Davide Calabria, 24 Simon Kjær, 46 Matteo Gabbia, 19 Theo Hernandez; 4 Ismaël Bennacer (Sandro Tonali 84), 79 Franck Kessié, 10 Hakan Çalhanoğlu (Brahim Díaz 84); 7 Samu Castillejo, 56 Alexis Saelemaekers (Rade Krunić 74), Zlatan Ibrahimović 

Referee: Adam Farkas (HUN)