Goals from Carlos Tevez (penalty), Emmanuel Adebayor and Craig Bellamy sealed a vital 3-1 victory for City after John Carew had put Villa ahead at Eastlands on Saturday afternoon.
"The players played a good game after 1-0," Mancini said.
"After Villa scored we continued to play well and scoring two goals before the end of the first half was most important.
"It was a difficult game as Aston Villa are a good team and they are not an easy team to play against.
"I think we must beat Tottenham. "It will be a massive game and we need all the supporters.
"It will be a fantastic game on Wednesday."