Gary Harkins hit the post for Killie eight minutes before the break, shortly before Manuel Pascali had a goal rightly disallowed by referee Craig Thomson for leaning on his opponent.
But Kilmarnock goalkeeper Anssi Jaakkola made the three best saves of the game, pushing past Chris Humphrey's early drive and then stopping Steve Jennings and Michael Higdon netting in quick succession in the 54th minute.
"I thought we started really well, got in behind them and got balls in across the face," McCall said. "We had a couple of chances. They came back into it and Harkins hit the post. The second half, we weren't at our best, there is no doubt about that. But we can't be at our best week in, week out.
"I was delighted with the way we defended. Although they had a lot of possession we snuffed it out and big Daz (Darren Randolph) hasn't had a lot to do.
"I said before the game they are a good side, you don't score three goals against Celtic if you're not. I think a draw was a fair result, there is no doubt about that. The only disappointing thing, we had a lot of set plays and we've been good at them recently, but the final ball wasn't as good as we would have hoped, in the second half anyway."