The City boss says the current Premier League standings are not a true reflection of his squad's form, but urged his players to try and reduce the deficit before the season's end.
The reigning champions have won three of their past seven league outings, and travel to Old Trafford on Monday to face a team unbeaten since Nov. 17.
Mancini acknowledged United’s impressive run of form - the league leaders are currently on an 18-game unbeaten streak that includes 16 victories - but has urged his squad to not give up on the title and aim to close the gap before the end of the season.
"We do not deserve to be 15 points behind," Mancini told reporters. "United have played very well and won a lot of games. They are unbeaten in their last 18 games in the Premier League. Their last defeat was at Norwich. So they deserve to stay at the top. But not by 15 points. It's not a true table.
"Now we have eight games left. If we play well and win a lot of those games, maybe we can reduce the gap. This should be our target at the moment."
The Italian also spoke of his delight that influential midfielder Yaya Toure signed a new four-year contract on Thursday, hailing the Ivorian as one of the top talents in the world.
"I am happy because for me Yaya is one of the best players in the world," Mancini said. "He's very important to this club. Yaya is a player who can play to 36 or 37, because he can play in central defense or just in front of the defense."