City draw 0-0 with the Reds at Eastlands on Sunday and Mancini claims the race for the fourth spot is in their hands.
He told Sky Sports: “Liverpool is a fantastic team and they would like to have won this game but in the end I think that the result is right because we didn’t concede any chances to Liverpool for a goal and Liverpool didn’t concede any chances to us.
“I would like to win this game, I think that (Rafa) Benitez would have liked to win this game.
“But I think that it was a hard game for both teams, in the end the result is okay.
“There are three teams, Chelsea, Manchester United and Arsenal (that have a chance) for the first three positions.
“Another four teams that can play for the last position, for the Champions League.
“It depends on us because we have 12 games, starting against Chelsea on Saturday.
“But we are in a good position, we must play, we must improve if we want to have that.”