The Turkish champions play host to the Premier League leaders on Wednesday in the first leg of their last-16 clash, and former Manchester City boss Mancini is fully aware of the threat posed by Jose Mournho's men.
The Italian coach feels the Turkish giants must focus on at least giving themselves a chance ahead of next month's return meeting at Stamford Bridge, but admits that the Europa League holders are undoubtedly favourites.
"Everyone knows Chelsea are one of the best teams in Europe," Mancini said. "They won [the] Europa League last year and [the] Champions League two years ago. They are used to playing these games every year and we know it will be difficult.
"I think Chelsea are top of the Premier League because they are a top team, with good players who can change the game at any moment. I think they are 80% [likely] to go through in this game.
"It's important we play well in this match because we want to play the return leg in London with some chance."
Much has been made of the tie reuniting striker Didier Drogba with his former club, whom he led to Champions League glory with the winning penalty against Bayern Munich in his final Blues appearance in 2012.
Yet Galatasaray midfielder Wesley Sneijder will also be coming up against a familiar opponent, having won the Champions League under current Chelsea boss Mourinho during the duo's time together at Inter.
"Well, what can I say about him? We won this cup together," the Dutchman told Uefa's official club website.
"Of course we are friends outside the pitch but tomorrow [Wednesday] for 90 minutes we will not be friends. I respect him a lot as we all respect him and respect Chelsea. We want to go for the victory but with respect.
"Of course I have some special feelings with Mourinho because we won the treble and had a great year together.
"It's going to be a tough game but we have prepared well and we will see what happens - we feel really confident.
"If we are all 100%, we can achieve something."