The Scottish champions picked up an important victory despite the Dutch side dominating possession for long spells, but the manager has played down their chances of qualification
The Scottish champions emerged from their opening Group H games against AC Milan and Barcelona without a point or a goal to show for their efforts.
Goals from James Forrest and Beram Kayal were enough to secure victory, despite Nir Biton's late red card and Lasse Schone's even later goal.
"I said Ajax would give us problems, as many problems as Milan and Barcelona, and that proved to be the case," Lennon told Sky Sports after watching Ajax leave Celtic Park with scant reward for long periods of possession.
"That's a fantastic win for us. We're on our knees at the minute in terms of our squad being really stretched so it was a monumental effort from our players."
Celtic are now third in Group H with three points, two clear of Ajax and as many behind Milan following the Italian side's 1-1 draw with leaders Barcelona.
A victory in the return match in Amsterdam would leave Celtic firmly in the mix for qualification, but Lennon is realistic over that prospect.
"That’s a big ask," he added. "I needed my goalkeeper (Fraser Forster) to make a great save just before we got the second goal but second half we were a lot better
"We didn't keep the ball in the final third well enough in the first half for my liking but we grew into the game and but for a couple of breakaways near the end we could have won it more comfortably."
Following Stefano Denswil's foul on Anthony Stokes, Forrest endured a lengthy wait to take his vital penalty as the ball was re-spotted and three yellow cards were dished out for dissent.
Nevertheless, the recalled winger impressively kept his cool to convert the first goal of the night.
"I was just focused on where I was going to put the ball and I'm glad it went in the back of the net," he told Sky Sports.
"It's brilliant to be back, obviously to score on the night and get three points on the board and we're looking forward to our next game when we play them away."
Forrest drew praise from team-mate Charlie Mulgrew for staying calm amid a typically boisterous atmosphere at Celtic Park.
"It's always good to get a goal before half-time and fair play to James," he told Sky Sports. "There was a lot of pressure on him after a long wait. He put it away brilliantly.
"We always knew this would be a massive game. After not picking any points up we knew we needed three points if we want to progress and we went all out to do that.
"It was a good two goals and a good result for us."