The champions are nine points behind Manchester United after a comedy of errors saw them lose 3-1 against Southampton at St Mary's on Saturday.
Sir Alex Ferguson's league leaders will go 12 points clear if they beat Everton at Old Trafford on Sunday, and Mancini is resigned to his team losing its Premier League crown.
He told ESPN: "I think now we have a 10% chance maybe. I don't think that we'll recover 12 points; it will be really difficult."
Mancini also felt the performance against Southampton was one of the worst in his time at the club and bemoaned the absences of the injured Vincent Kompany and Matija Nastasic.
Asked what he said to his players after the match, the Italian added: “Nothing. I think they understand that we played really badly. I think this the worst game in the last two or three years.
“We’re missing Vinnie [Kompany], we’re missing Nastasic, and we have some players who are not in form because they played really badly; without strength, without personality, and I’m disappointed with them.”