The Buddies were set for a point after Adam Campbell's debut goal, but Kris Boyd's injury-time strike won it for Killie.
"That was a sore one to take and we're very frustrated and disappointed with the result," he said.
"You wonder how you lost it but if you give someone as prolific as Kris Boyd an opportunity then he can punish you.
"I thought we handled him for the 90 minutes but failed to do so in the two minutes added on. You've got to have the highest levels of concentration when you're playing against someone of that quality.
"I thought wee Adam Campbell gave a great flavour of what he's going to bring, not just for us but to Scottish football as a whole. He's got lovely soft feet, a lovely touch and good pace.
"He's going to grow in confidence. It will take him a bit of time to settle into our game up here but that performance from him today - and the goal that he scored - will give him added confidence along the way."