City were made to earn their three points in the 3-1 victory over Mick McCarthy’s visiting side and Mancini was happy to see his players work and toil after some seemingly easy wins of late.
"It is impossible to always score four or five goals,” the Italian said.
"I don't know how many chances we had in the first half today, but their goalkeeper saved everything. But in the second half I think we played very well and it was important to beat Wolves today.
"After the Man United win I don't want us to think that every game will be easy. This does not exist in football, in every game you must give 100% because if not, like today, in any moment the game can change.
"After the sending-off (of Vincent Kompany) it was very difficult."
Edin Dzeko, Aleksandar Kolarov and Adam Johnson all scored second-half goals for City as Stephen Hunt netted from the penalty spot in the 75th minute after Kompany was sent off for bringing down Kevin Doyle in the area when clear on goal.