Sean Dillon scored the visitor’s goal after Gary Hooper's 23rd minute opener - his 11th goal of the season - looked to be enough to keep the Hoops right on the tails of the champions who had won 3-2 at Kilmarnock earlier in the day.
"You have to recognise important moments in the game and when you are one-nil up deep in to injury time you have to see it out," Lennon said.
"I can't keep saying it's a learning experience because I haven't got time to keep saying that.
"It's galling to drop points but the gap is not insurmountable. It's only three points and our goal difference is still pretty healthy.
"But the players need to learn from this. There is a mentality you have to have and you need to see games out.
"We didn't do that.
"We've gone to ground for the free kick before the goal.
"I'm sure if it was a free kick but you shouldn't give the referee the opportunity to give the free kick.
"It's cheap and it's annoying.
"If you give silly free kicks then you are asking the ball to get put in your box."
He added: "We defended set-pieces well but we should have been strong enough to see it through.
"At that stage of the game you should be throwing yourselves at things.
"What galls me is that it is a free header in the six yard box in the middle of the goal.
"From our point of view that is unacceptable.
"However, there were lots of aspects of the game that pleased me and we should have put the game to bed."
United boss Peter Houston claimed his side might have left Parkhead with all three points but Lennon retorted: "He must have been watching a totally different game from me.
"Who was the busier keeper? David Goodwillie had the best chance of the first half but after that it was chance after chance for us.
"We had one cleared off the line, Pernis had made two or three saves so I don't buy in to that."
Houston, though, was adamant that his side deserved at least a share of the spoils.
"I thought that was the least we deserved," the Scotland assistant manager said. "I would have been very disappointed had I been sitting here talking about a one nil win for Celtic.
"There's a slight tinge of disappointment that we only got one point because we had good chances.
"Perhaps we could have had a couple of goals before Celtic scored. We lost a good goal from Celtic's point of view and then Dusan Pernis made a great save to keep us in it but I don't think he had many saves to make in the second half.
"I felt there was a goal in us today. We kept our shape but we were a threat going forward.
"It was a case of better late than never."