The Rossoneri have not won in seven games and know that a defeat in Glasgow would seriously jeopardize its 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 its own fans, who blocked all of the exits at San Siro with the intention of forcing the players to come out to face them.
Kaka went along with goalkeeper Christian Abbiati to appease the ultras, and the attacking midfielder freely admits that Milan desperately needs a positive result in Glasgow to not only maintain its grip on second place in Group H but also appease its supporters.
"At the moment, the big problem is that we cannot win," the Brazilian said. "[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."
Kaka said Milan's players are used to playing matches in which the stakes are elevated.
"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," he said. "The atmosphere [at Celtic park] is amazing. A few of my teammates have played here before. It is never easy against such a great support. It will be the same [on Tuesday]."
Milan goes into the game with five points, one more than third-placed Ajax, which hosts group leaders Barcelona in Amsterdam, and two clear of Celtic.