Saints recorded a sixth successive clean sheet but were denied a sixth consecutive victory by a resolute Rugby Park rearguard.
Home winger Matt Kennedy hit the post with a late curling effort and goalkeeper Zander Clark, pictured, preserved his shut-out record with a superb diving save to deny Greg Stewart.
Clarke felt Killie could have sneaked a win on the balance of play and was disappointed not to have been awarded a 75th-minute spot-kick when Joe Shaughnessy bundled over Kris Boyd in the box.
He said: “I’ll probably let the guys from television go through it and tell us it was a penalty but we didn’t get it. It looked as if he was wrestled to the ground, so on another day we might have got it.
“Listen, referees make the decisions and you’ve just got to get on with it. But it was a decent shout for a penalty.”
Clarke added: “I think we probably shaded it on the balance of play. But the other thing I would say is that we didn’t do enough in the final third.
“We got into some really good positions but we didn’t do enough to work their goalkeeper often enough. Although, when we did work him, he made a hell of a save.
“But they will probably point to the one where the guy’s cut in off the line and hit the post with the shot. I suppose three weeks ago, if you had said we would go to Tynecastle and to McDiarmid Park and take four points we probably would have settled for that.”
St Johnstone boss Tommy Wright was disappointed with elements of his side’s play, and to see their winning run come to an end, but felt a draw was the right outcome.
Only one point separates the teams in the Premiership table and Wright said: “I think a draw’s the right result. We knew it was going to be a difficult game; they certainly set out to frustrate you and they did that to us today.
“I’ve got to give them credit for that, they’re a good side.
“We’ve kept six clean sheets in a row, we’ve kept the run going and we’ve maintained fifth place in the league and moved closer to Hearts. So it’s been a good day.”