Celtic had been beaten by Barcelona and AC Milan in their opening two fixtures but kept their hopes of a place in the last 16 alive with a hard-fought home win.
James Forrest's penalty and Beram Kayal's strike did the damage for the Bhoys, before Nir Biton was sent off in the 88th minute and Lasse Schone's stoppage-time reply for Ajax.
Manager Lennon was proud of his players but would not go as far as saying they could win in Holland, with Ajax now bottom of the group on one point and Celtic just two behind second-placed Milan.
"I said they would give us problems and our squad is stretched, so that's a fantastic win for us and a monumental effort from the players tonight," Lennon said.
"It's a big ask (to win at Ajax). They're a good side.
"We needed our goalkeeper to make a great save just before we got the second goal, but I felt that in the second half tonight we were a lot better.
"We didn't keep the ball well enough for my liking in the first half but we grew into the game."
The Celtic boss added: "It leaves us in a very good position.
"We will have to get a result in Amsterdam and that is going to be very difficult on tonight's evidence but it is not beyond us.
"We have three points, just two points behind Milan so the group is open for us again."
Lennon, who insisted Kayal was "worth his weight in gold" for his goal and a saving tackle on Viktor Fischer in the first half, praised Forrest's bravery in taking the penalty when regular spot-kick taker Kris Commons was out through injury.
The former Celtic skipper said: "He keeps telling me he has never missed a penalty so this morning we had a chat and he said he would take it, because obviously Kris was out.
"He kept his cool because obviously there was a lot of gamesmanship going on from the goalkeeper but he kept his cool.
"It was a big moment in the game, just before half-time and it set us up very nicely for the second half."
On Biton's ordering off, Lennon said: "I had no complaints. He was late. I'm not convinced there was contact but he left a trailing leg."
Ajax boss Frank De Boer remains confident that his side can still get third place in the group.
The former Rangers player said: "Celtic didn't create anything although they scored twice, once with a penalty.
"We dominated the game but only scored once and should have equalised before they got their second.
"It is going to be very hard for us to get second place but I have confidence in the third place.
"We have one point and if we win at home we will be one point ahead of Celtic.
"It will be difficult but if we play that way again...eight times out of 10 the best team wins and I thought we were the best team.
"But only goals count and we will have to do it in the Arena."