Buddies debutant Esmael Goncalves gave Saints the lead in the eighth minute, but that was cancelled out by Gary Hooper a minute from the interval.
Craig Samson saved Charlie Mulgrew's penalty four minutes into the second half and things got worse for Mulgrew in the 83rd minute as he handled a Gary Teale cross inside the area, which allowed former Celtic man Paul McGowan to score from the spot before former Rangers striker Steven Thompson grabbed a third.
Mulgrew ended a desperate afternoon by scoring with the last kick of the match, but it was not enough. And after seeing hopes of a domestic treble ended, Neil Lennon was scathing in his assessment of his side's performance and their mentality.
"I am bitterly disappointed with that performance," he said. "It was soulless, it lacked intensity, desire and will to win, all the attributes this team has shown over the last six to nine months.
"That was an impersonation of a team that I know. There is not one player, maybe with the exception of Hooper, that would get pass marks.
"There was a lack of discipline in our shape and play. I thought we were defensively awful, the decision making was poor and the there was a lack of quality in the final third.
"Some of them behaved like spoiled kids out there. The treble is gone, we have only ourselves to blame. The criticism is going to come our way and rightly so. Hampden seems to be a bogey ground, but to be fair that's the worst we have played here.
"I can take losing to Kilmarnock in the final and in the semi-final last year (against Hearts) because our performances were decent, but that was awful today from what I perceive to be top-class players. But maybe I have got it wrong and maybe I have to look at this week and change things, I don't know.
"I'd like to congratulate Danny and his team, he is a good guy in the game. I don't want to take anything away from them, but I cannot be too enthusiastic about our performance."