Charlie Mulgrew rescued a point in injury-time for the unbeaten league leaders, who made four changes from last weekend's Glasgow derby win over Partick Thistle.
Despite dropping two points, Lennon remains upbeat with the news that Kris Commons, Georgios Samaras, Beram Kayal, Mikael Lustig and James Forrest are all available for Wednesday's Champions League clash with Ajax.
"I'm very happy that we got something we deserved," said Lennon. "I should take the criticism if there's any coming our way because I picked the team.
"I wanted to use the squad for this game, with a huge game on Wednesday. I made four or five changes, which isn't ideal, but players need game time.
"I know some of them are a little short because of the injury problems we've had but Lustig will come through okay, Kayal will be fit, Georgios Samaras and Kris Commons will be fit, so we'll be a lot stronger on Wednesday.
"So I'll take a point. It preserves the unbeaten record which obviously we're very proud of but we were a bit flat and certainly in the final third we need to do better.
United boss Jackie McNamara feels a late miss from Brian Graham to double the lead cost his side a chance to win at Celtic Park for the first time since 1992.
McNamara said: "I think Brian was in two minds how to take it, although that possibly could have killed the game for us.
"He mentioned it when he came off, it was obviously playing on his mind but to be honest I thought he was excellent. His play deserved a goal.
"It shows how far we have come when we are disappointed to go away with a point."