Midfielder Ryan Christie opened the scoring for the champions behind closed doors in Ayrshire on Sunday after 10 minutes with a kick-free kick from a distance.
However, Killie’s veteran winger Chris Burke tied in the minute with a penalty conceded through Hoops’ central defender Christopher Jullien, who committed a foul on striker Nicke Kabamba in the area.
Celtic will face St Mirren on Wednesday, Aberdeen on Saturday and KR Reykjavik the following week in their first Champions League ranking.
Lennon told Celtic’s official website: “We don’t think an upcoming game is easy, I don’t take anything for granted.
“We lost a few points, which is disappointing, but we have a long way to go and the team will do it as we pass.”
“We look to Wednesday’s game when it arrives and we’re in favor of a smart performance.
“We hope Reykjavik is a home tie, that’s all you can ask for, really. We can’t wait to get back to Celtic Park.”
“Sometimes it’s complicated without the enthusiasts. If you look at the middle of the moment, there were times when enthusiasts would have made the team move forward, but we have to adapt.
“Like I said, I don’t think it’s a bad performance, it’s just a little bit missing the sharpness we have.”