The Celtic boss tried to take some of the pressure off his men by reminding them this is the first of a six-game league - not knock out.
To that end, Lennon insists they don't need to take all three points - but added they will be trying to do precisely that.
He believes the toughest part of any European campaign is the qualifiers and play-offs, when one slip can spell the end of the dream, and £15million.
Now they are back in among the big boys in the group stage, a completely different mindset can be adopted.
Lennon watched his side come close to taking all three points in Barcelona last season, only to be pegged back at the death by Messi and Co.
He does not want to go through such agonies again and said ahead of their opening tie: "We don't have to win it.
"I would love us to win, but, more importantly, I want to see a performance.
"And I don't want us to be gallant losers, either.
"I want us to go to the San Siro, play strongly, and play with the maturity we are starting to show."
Lennon has updated his players on the opposition after watching Milan battle back to draw 2-2 with Torino in Turin on Saturday night.
He watched Kaka limp out of the action, and contention for tomorrow's tie, with a muscle strain.
But even though the Brazilian has now joined a galaxy of stars who will be missing from Milan's line-up, Lennon still concedes the Serie A giants will carry a massive threat.
That could come, in particular, in the form of Mario Balotelli.
But Lennon is confident his own team is capable of continuing last season's excellent away from in the group stage of the Champions League and once again get on the score sheet.
He is still waiting to see if James Forrest has fully recovered from the sciatic nerve problem which sidelined him at the weekend.
But even if the Scotland winger fails to make it, the Hoops can still utilise pace through Derk Boerrigter.
The Dutchman's height will also be a potent weapon in Celtic's armoury, and Lennon is tipping the former Ajax player to make an impact in this tie.
Lennon said: "What Derk gives us is a quick leftie, with a bit of quality. He'll go beyond players and does make good runs off the ball.
"It is a little bit different from what he was used to playing at Ajax in a rigid 4-3-3.
"Sometimes he is making runs in the park when we want him to stay just a little bit wider. But once he got adjusted to it on Saturday at Tynecastle, I thought he had a very good game."