The Italian side arrived in Glasgow for Tuesday's match on the back of dismal domestic form, with pressure from the fans mounting.
Milan have failed to win in their last five league games and sit a lowly 13th in Serie A, and Kaka knows how crucial victory against Celtic could be to their last-16 chances and boosting their season as a whole.
The Italians are in second place in Group H, but just a point ahead of Ajax and two ahead of Celtic.
The midfielder said: "This is going to be a very difficult match but, by winning tomorrow [Tuesday], we could kickstart our season.
"We could even qualify if we win and the other result goes in our favour. This match could be a turning point in our season.
"It's definitely a challenge to put indifferent form and off-field problems to the side.
"We've got to try to have a good season and to do as well as we can on all fronts."
Kaka and goalkeeper Christian Abbiati spoke to furious fans outside the San Siro following their 1-1 draw against Genoa at the weekend.
He said: "Speaking to the fans the other night wasn't a huge burden to me.
"It's not something I'm used to doing, but if I'm seen as one of the senior players in the squad then I have to get used to this type of responsibility."
Asked about the morale in the camp ahead of the match with Celtic, Kaka said: "At this moment, the atmosphere is a little tense.
"But that's not bad sometimes. Sometimes it's a motivation, when you use this tension and pressure.
"We are always under pressure at Milan. We are seven matches now without a win and the pressure to end that bad run certainly gets more and more.
"This is an important match and we have to be mentally ready for it against what will be a difficult opponent."
Milan coach Massimiliano Allegri denied failure to secure a win, and book their place in the knockout stages, would cost him his job.
"Not at all,'' he said.
His Celtic counterpart Neil Lennon insists there is no chance of the Glasgow side underestimating the threat of Milan.
The Hoops boss said: "They could be a wounded animal and that's always a dangerous proposition no matter who you face.
"They'll have their pride. They have some world-class players, players who are class acts and who have been at the top level of the game for a concerted period of time.
"If anyone thinks that we are underestimating them and think it's a really good time and think it's going to be a comfortable home win, they'll have to think again. This team is dangerous."
The Scottish champions sit bottom of the pool but a win over Milan - combined with Barcelona denying Ajax victory - would see them move into second spot.
As far as Lennon is concerned, Tuesday's clash is now one of the biggest games of the season.
He said: "Certainly in the context of the Champions League it is. It's a game we have to win to have any chance of qualifying.
"It's a great game for the players to be involved in. We have performed very well in the group apart from the first half in Amsterdam so I want that to continue on Tuesday.
"I don't think we need much incentive or motivation for the game. We are playing against a very good side, despite what their recent league form is maybe showing.
"I watched their game on Saturday and they dominated the game against Genoa (1-1 draw) and were unfortunate not to win.
"Some of the football they played, and the tempo they played at, was of a very high calibre."