Mancini's men secured the victory thanks to a 63rd-minute goal from Joleon Lescott and the Italian hailed their efforts throughout the season.
"We were there (at the top) from August because we deserved this. It was a difficult game. We knew this before the game but the guys played fantastic football," he said.
City goalkeeper Joe Hart made some crucial saves late on to preserve the Blues' lead but Mancini insists he is not the best in the world - yet.
"He's very young and there are other keepers with more experience," Mancini added.
"He has many years in front (of him) but he could become one of the top keepers. Joleon played fantastically as well, we played fantastic football in the first half and we were missing only a goal."
Carlos Tevez has not played for City since he refused to warm up during the Champions League defeat to Bayern Munich in September, but it is reported that he intends to return to England from Argentina on Tuesday and is ready to resume his City career after failing to secure a move away in the January transfer window.
Mancini told Sky Sports: "My reaction is always the same. Carlos knows the situation, we are here and it depends on him.
"Carlos knows the situation from September, we don't have any problem."
Asked if an apology was still what City were waiting for, the Italian added: "Yes, it's possible. For now we should be happy for this game. For Carlos' situation, we know what can happen. Carlos is a Manchester City player. We are in Manchester, we are always there. We have not changed in these three months, we are there."
Villa boss Alex McLeish told Sky Sports: "I thought the game plan was excellent but the players were unlucky. We're getting a lot of luck at the moment but it's all bad. Richard (Dunne) has hurt his shoulder, we lost Ciaran Clark yesterday [Saturday] with a knee ligament strain.
"The Villa fans stayed right behind us for the entire game and I thought we were very unlucky not to get anything.
"We must stop the errors - we had one lapse in concentration but we are playing a side vying with Manchester United for the title. Our home record is pretty abysmal. I'm disappointed with that because I pride myself in my managerial career with home performances and the current one isn't good enough."