European Ryder Cup captain Padraig Harrington admitted it was "incredibly difficult" to leave Justin Rose out of his side after selecting Sergio Garcia, Ian Poulter and Shane Lowry as his three wildcards.
Bernd Wiesberger's tie for 20th in the BMW PGA Championship saw him secure a debut at Whistling Straits at the end of the month, knocking Lowry out of the side.
Lowry could have replaced Lee Westwood with a top-eight finish and began the day in a tie for seventh, but faded to a tie for 17th with a final round of 71.
Westwood therefore qualified for a record-equalling 11th Ryder Cup despite a closing 77, the 48-year-old joining Wiesberger, Jon Rahm, Tyrrell Hatton, Paul Casey, Rory McIlroy, Matt Fitzpatrick, Tommy Fleetwood and Viktor Hovland in the team.
Rose eagled the 18th in a final round of 65 to finish in a tie for sixth, but that was not enough.
"It was incredibly difficult with JR," said Harrington. "Clearly he was in contention in his last two events.
"Did I need more? Maybe not but the fact of the matter is, with who he was going up against, the consistency of Shane Lowry, the heart of the team has been Ian and Sergio over the years, somebody had to lose out.
"It really is as close as that. If you don't play your way in it’s a tough place to be. It easily could have been JR or Alex Noren.
"I’m delighted for Bernd Wiesberger. He’s a great player and anybody who makes their way into the team fully deserves it, but ultimately it was a spot gone that could have gone to a JR or an Alex Noren.
"I had a chat with him (Rose) and he was an absolute gentleman. I certainly would have been happy with him there but it was just one spot too far."
Speaking before the announcement was made, Rose said: "It would be disappointing. You reflect on why. Is there something bigger at play because on the surface I feel pretty confident.
"I think it will be hard for him not to pick me but I had that with Monty (Colin Montgomerie in 2010), as well, and it went a different way.
"From my point of view, you can only blame yourself if you don’t get in and don’t get picked, because obviously I’ve never had a pick for the Ryder Cup."
Poulter, who has now been picked as a wild card five times, said: "I feel for Justin. We all know what a class golfer he is.
"It’s a hard call to take from the captain. I’ve been in that situation myself a couple of times and the last thing you want is to be on the outside looking in."
As for his own selection, Poulter said: "It’s surreal. To know we are going to go again is amazing. This trophy has meant a lot to me through the years. For Paddy to call me and say 'I want you to be part of my team’ – it’s emotional.
"It’s an honour to get a pick. The focus the next seven days gets ramped up.
The mindset changes, the phone goes off, not so much social media until it’s go time."
Lowry had made no secret of his desire to make the team, but had hoped to qualify automatically and avoid the need for his good friend Harrington to give him a wild card.
"It’s been a career-long dream to play in the Ryder Cup," said Lowry.
"I remember when the points race started here, I said it was my number one goal and it has been for the last two years.
"I’m just incredibly proud of what I have achieved. But there’s no point going over there to make up the numbers. I want to win points and help bring the cup back."
Garcia, who is the record points scorer in the Ryder Cup with 25.5, said: "It feels amazing. Just can’t wait to get there, see the guys and get going.
"To be able to win six Ryder Cups, to me that’s more important than 25.5 points. I would rather go 0-5 and win the Ryder Cup than 5-0 and lose. That’s never going to change."