Defender Mikael Lustig fired in his first Hoops goal in the 11th minute but a disastrous mix-up between the Swede and keeper Fraser Forster allowed Tim Clancy to equalise. Lustig helped force in a second via Hibs skipper James McPake but again poor defending by the champions allowed Paul Cairney to level with a drive.
"Barring the two goals I was pretty pleased with the performance," he said. "We murdered them first-half but if you miss easy chances and if give away the goals of the nature we gave away you are always fighting to win the game. But I am not angry, I am just a little bit annoyed."
The Hoops boss added: "We missed simple chance after simple chance and we can count ourselves very unlucky not to win the game today. We should have been out of sight at half-time. On chances alone we could have won two games."
Lennon stressed he was not concerned with the goals lost, particularly with the better class of opponents looming in Europe.
"It is very unlike us," he said. "It is just a lack of concentration. Obviously it is a mix-up for the first goal and we missed two tackles for the second and the players know that can't happen at any level.
"I am not going to point the finger of blame at anyone, they were just poor goals lost by players who have been superb for two years here so they are allowed a bad day at the office. I think the result flattered Hibs today."
Hibs manager Pat Fenlon claimed his side showed the character that was missing last season.
"We have a different type of character in the dressing room at the moment, a different type of animal altogether that wants to scrap and fight for each other," he said.
"We knew at half-time we had got away with it and we rode our luck at times but if you can get back into the game it can get a little bit edgy for Celtic. You have to get a little bit of luck to come here and get any type of result but I thought we played really well in the second half."