An own goal from Jamie Adams and a strike from Jim Goodwin helped the Buddies claim their first victory in 14 attempts against St Johnstone.
And the hosts' boss was not pleased to see his team's five-game unbeaten run come to an end in such limp fashion.
"The damage was done in the first half and I felt the better team won," he said. "I thought we never really treated it like a cup tie until it was too late.
"We've got a lot of injuries at the moment, we just looked off it, compared to where we have been.
"St Mirren deserved to go through, there are no complaints from us other than the fact we're disappointed with our own performance."