After losing twice to their close rivals in the league last season - not to mention the Carling Cup - the Italian felt his team had taken a step forward.
Asked whether City were getting closer to United, Mancini said: "I think so. We just need more time. We are improving. I prefer one point to zero points, which was the case last season."
He added: "When you play in a derby it is a difficult game. We did not have many chances to score but it was a good point.
"We tried to win but they defended very well. We play to win but when you do not have many chances it is difficult."
Former United striker Carlos Tevez came close to making the breakthrough with a superb free-kick in the first half after shrugging off a thigh injury.
Tevez's effort cleared the wall but Edwin Van der Sar pushed the ball to safety.
Mancini praised the Argentina striker, who had little support, after he returned on Sunday from a break to help the team beat West Brom.
"Carlos is an important player for us," Mancini said. "He played well against a strong defence. He ran well although he may have been a little tired like some of the other players.
"When you play every three days it is not easy, especially when you have to play a derby game."
Source: PA
Source: PA