The Italian saw his side run out as impressive 4-1 winners against Aston Villa at the Etihad Stadium to leapfrog Sir Alex Ferguson's side and take top spot in the table
Goals from Mario Balotelli, Adam Johnson, Vincent Kompany and James Milner secured all three points for the Italian's side, which leapfrogged city rival United following its 1-1 draw with Liverpool at Anfield on Saturday.
"We've only played eight games and there are 30 to go," he said. "We should be happy to go to Old Trafford on the top but we should understand that the championship will be long and that this position can change every week. We have started very well and won a lot of games but we need to improve more."
The home side was impressive against Alex McLeish's men but Mancini, who jokingly booed an announcement from the City press officer stating that no questions could be asked about the Carlos Tevez saga, admitted the Blues started somewhat sluggishly.
"We had a problem in the first 15 minutes because when the players come back from an international break it is always difficult," he said. "But I think after 15 minutes we played very well, Mario [Balotelli] scored a fantastic goal and I think that changed the game. We started the season very well, we knew that this week would be hard because we played Aston Villa and then we play Villarreal which is a crucial game for us and then we have the derby, so our mind is very busy."
Balotelli's opener continued his fine form in the absence of both Tevez and Sergio Aguero, and Mancini was full of praise for the Italian youngster.
"I think that Mario is always happy," he continued. "He had four or five matches on the bench but I think he understood. He has played well, he has scored in four games in a row but Mario can change in every moment. He's worked well and played well. He's motivated, he's playing, he is scoring and it's an important moment for him."