The Jags appeared to be heading for their first home win of the season until Robbie Muirhead snatched an equaliser in added time after stand-in goalkeeper Paul Gallagher had blocked Kris Boyd's penalty.
The Killie boss was delighted with his team's second-half performance, and he feels the likes of 19-year-old Chris Johnston and his young colleagues like Craig Slater and Muirhead need more encouragement.
"This is a big point for us," he said. "The boys showed a lot of character to come back, especially because I don't think they got the backing they deserved to be honest.
"We have a lot of young boys and they need encouragement. The last thing we want to do is to get their heads down as soon they make a mistake, so we need the fans to get right behind them.
"I'd rather they got behind the team. That's the most important thing. It won't help getting on their backs.
"Do the fans need to show patience with the young lads? Aye. You are going to get performances where the team is up and down with their age, but we saw the character that they have got. They didn't let it affect them and got their rewards."
Partick were agonisingly close to jumping above Kilmarnock in the table, but they have now dropped into the relegation play-off spot following yet another missed opportunity at Firhill.
Manager Alan Archibald, whose side blew a two-goal lead against Ross County last week, said: "It's the same old story. I said the same things last week and I could say the same this week.
"It was a very, very good performance at the start, but I'm very, very disappointed with the way we finished it.
"I thought we were scared of winning last week, but I didn't think that was the case this time. I just thought we made a mistake for the goal. We had two midfielders go for the one ball and that was what led to the goal and that's what is hard to take.
"I'm disappointed for Paul Gallacher because no-one has reacted. He helped his back four out by saving the penalty, but there wasn't a quick enough reaction to get on the rebound."