The Hoops reached the lucrative group stages of the competition for the second successive season in dramatic style on Wednesday night when they beat Shakhter Karagandy 3-0 to knock the Kazakhstan champions out of the play-offs 3-2 on aggregate.
Their reward was to be drawn against three of the biggest names in European football in what Lennon described as the "best and worst" of groups.
The Scottish champions reached the last-16 of the competition last season, beating Barcelona 2-1 at Parkhead on the way, but the Celtic boss does not believe that means a repeat should be expected.
"I said at the beginning of the tournament it would be very difficult to emulate what we did last year," he said. "I think qualifying for the group stages was huge for us.
"If we can get anything else out of it, then so be it. You just never know with this bunch of players what they are going to bring - we could get no points, we could 10, you just never know.
"But the pressure is off in terms of I don't think anyone really has huge expectations on us to qualify, although some of our fans who set very high standards will be expecting that."
Lennon acknowledged the status of the Hoops' opponents but is looking forward to six memorable group games.
"It's obviously very exciting," said the former Celtic skipper.
"In terms of glamour, you couldn't have asked for anything more and in terms of difficulty you couldn't have asked for anything more.
"Ajax were with Dortmund and Man City last year and came third in the group. Milan have been in transition but are coming on strong again.
"They beat a very good PSV (Eindhoven) team to qualify so pedigree is unquestionable. And we're going to see our old friends Barcelona again.
"The experience of last year will stand the players in good stead."