Former Celtic striker Chris Sutton is not convinced their 12th consecutive trophy will be the catalyst for another successful season after branding their defence among the worst in the club's history.
Neil Lennon's team clinched the quadruple treble after beating Hearts 4-3 on penalties in last season's delayed William Hill Scottish Cup final but their defensive problems were there for all to see.
Hearts came from two goals down to force extra time and levelled again in a dramatic 3-3 draw, with two of their goals coming from set-pieces and another from a cross and header.
Goalkeeper Conor Hazard became a hero on his third appearance when he saved twice in the shoot-out but he failed to convince coming off his line during the game after being preferred to Vasilis Barkas and Scott Bain.
Ireland international Shane Duffy again had a torrid afternoon in central defence and Sutton feels the cup victory will not make a massive impact on their faltering 2020-21 title charge.
Sutton said: "I thought they were fortunate. I didn't think Hearts deserved to lose the final in any way, shape or form.
"And the hope now is this team can kick on. If I'm honest, I'm not convinced, because defensively it's been the Celtic this afternoon which we have seen all season.
"They don't see games through. It's possibly one of the worst defences in the club's history."
Former Celtic boss Martin O'Neill, who won the treble with Sutton and Lennon in his team in 2001, admitted his former side looked fragile at times.
But he urged them to use the triumph to refocus efforts on hauling back Rangers' 16-point lead with Celtic now having three games in hand.
O'Neill commented: "I don't watch Celtic all the time but enough to say that that performance, both halves, epitomised their game.
"There were some great moments in the match where they were full of confidence and feel as if they can beat anybody, and 2-0 up and absolutely cantering through.
"They concede a goal and instead of puffing out and saying 'OK, that's a mistake, it's gone', the fragility comes into their play. And the next thing you know they are hanging on and Hearts, like other opposition, have seen this fragility and they go for it.
"That's what has happened on a number of occasions. Celtic have had some great moments in matches, even in European games for half an hour.
"But certainly now, they should push this aside. It's great, the quadruple (treble), something that will never be achieved again - certainly not in my lifetime, I can tell you that for an absolute certainty.
"They can try and push on. It was a big win yesterday for Rangers, that opened up a big, big gap. But this competition is on the sideboard now and just go for it, go for it as much as you possibly can. It's a long way back but it still can be done."