First-half goals from Samuel Eto'o and Gary Cahill earned Chelsea a 2-0 win at Stamford Bridge on Tuesday night to complete a 3-1 aggregate success over Galatasaray.
Chelsea currently lead the Premier League, but are in a four-way battle to win the title, alongside Liverpool, Arsenal and City.
Mancini expects Chelsea and City will be the last two left standing, but the Galatasaray coach has suggested his old club have the better team.
"I think that Manchester City's the best team," Mancini said. "They have the best players.
"I don't know if Liverpool, also doing very well in this moment, can win. I think it will be a fight till the end between City and Chelsea."
The Italian was unhappy with his team's performance against Chelsea after Galatasaray, with former Blues striker Didier Drogba in attack, rarely threatened.
He added: "The game was difficult. After we conceded after four minutes it was even more difficult, but this doesn't change the fact that we played really badly - we didn't deserve anything and Chelsea were much better.
"It is difficult to say something about the game because I am very disappointed that we didn't play well. We didn't create chances. I am very sorry for our supporters because they were the best players for us - I am very disappointed for them.
"I don't know why, it is really difficult to explain. After the game in Istanbul I was confident we could play here and have a chance to score. Our football was totally different and if we want to play at this level we need to work more.
"We prepared for this game. We started from 1-1 and it was really important to start this game and not concede a goal. Instead, we conceded after four minutes and that made it very difficult. We knew it would be a difficult game, but we knew we had a chance. I am very disappointed."