Lasse Schone notched the winner six minutes after the re-start as Ajax claimed the three points to climb above the Hoops in Group H.
But Celtic's Beram Kayal and Anthony Stokes failed with opportunities to score, while James Forrest should have picked out Stokes in the 57th minute as he raced down the right but managed to hit Joel Veltman, the only Ajax outfield player back.
Lennon's side must now beat AC Milan at Celtic Park later this month to have any realistic hope of qualifying ahead of their last game against Barcelona.
He told Sky Sports: I thought we were poor first half, I thought we were a lot better second half.
"The goal came at a time when we were just starting to get a foothold in the game. That's a poor goal from our point of view.
"But we had chances second half, particularly the two v one with Jamesie breaking - you're thinking it was a great opportunity and that might have just changed the course of the game.
"But I thought we were second best first half and some players will have regrets about their performance tonight because they weren't anywhere near their best."
He added: "We've left ourselves a lot to do. The last game, at the Nou Camp, is not the easiest place to go.
"But there's still a lot to play for in the group."