The Hoops looked to be cruising with 10 minutes to go after Tony Watt had doubled the lead given to them by substitute Miku. However, in the final minute of normal time United substitute Gary Mackay-Steven pulled one back before Hoops substitute Efe Ambrose put a Barry Douglas cross past goalkeeper Fraser Forster in injury time.
However, the Parkhead boss was in forgiving mood, saying: "It is very frustrating because we were so good. We were excellent, the level of performance was very high. Our play in general was very good, so in terms of play and chances created, everything was there."
He added: "We didn't get what we deserved which was three points. But I am not going to criticise the team. There will be people out there who will criticise us but that performance was very good today.
"I am annoyed that we didn't see the game out, but that's football. We just switched off and let Dundee United get up a head of steam for two or three minutes and they got a lucky break for the second goal."
Lennon found himself with two additions to his injury list ahead of Wednesday's Champions League clash with Barcelona at Parkhead. Georgios Samaras (ankle), Gary Hooper (hamstring) and James Forrest (hamstring) all missed the trip to Tannadice while defenders Thomas Rogne and Emilio Izaguirre came off injured.
The former Celtic skipper said: "Thomas went off with a calf strain very early in the game and he is a doubt. Emilio is feeling his hamstring and again, he is a doubt. Forrest is also a doubt but we are hoping Hooper and Samaras will make it."
United boss Peter Houston insists he still believed his side could take something from the game when they fell two behind with 10 minutes remaining. He said: "All we needed was a wee break and when you get a goal with minutes to go it sets teams rocking. I have been in that situation and Celtic were on the back foot at the end.
"I felt it was no less than we deserved and if I am being honest I would have been disappointed if we had lost the game, so great credit to the players. Celtic had good possession in the first half but I don't remember our goalkeeper having too many saves to make.
"But we found ourselves 2-0 down but the players showed their character, they kept going to the final minute and maybe if the game went another five or 10 minutes we might have gone on to win it."
Source: PA
Source: PA