The Rossoneri have not won in seven games and know that a defeat in Glasgow would seriously jeopardise their chances of making the last 16
Saturday's 1-1 draw at home to Serie A rivals Genoa was the Rossoneri's seventh match in all competitions without a win and it provoked a furious response from their own fans, who blocked all of the exits at San Siro with the attention of forcing the players to come out to face them.
Kaka went to appease the ultras, along with goalkeeper Christian Abbiati, and the attacking midfielder freely admits that Milan desperately need a positive result in Glasgow to not only maintain their grip on second place in Group H, but also appease their supporters.
"At the moment, the big problem is that we cannot win," the Brazilian lamented. "[On Tuesday], we will try to win whether we have a good or bad game.
"It is very important for the group that Milan win three points. The atmosphere is a bit tense in the changing room but sometimes it is a motivation.
"We are always under pressure in Milan. Seven matches without a win, it means there is more and more pressure to win the next game. And it will be against a very difficult opponent.
"The atmosphere [at Celtic park] is amazing. A few of my team-mates have played here before. It is never easy against such a great support. It will be the same [on Tuesday]."
Milan go into the game on five points, one ahead of third-placed Ajax, who host Group leaders Barcelona in Amsterdam, and two clear of Celtic.