Hargreaves has been sidelined for virtually three seasons and was released by Manchester United during the summer.
"It was good for him," declared the Italian. "Owen is a fantastic player, who can become a very important player for us.
"He hasn't had any problems in the last three weeks. At the moment his knee is fine.
"We said before the match we would give him between 45 and 60 minutes. As it turned out, he was okay for 60."
Mancini must now decide the best way to plot Hargreaves' progress, knowing the new arrival will be denied an emotional reunion with former club Bayern Munich in the Champions League next week as he was not registered in City's 25-man European squad.
"We didn't know what his condition would be when we had to decide," said Mancini. "It was difficult. It is possible we could bring him in during January.
"But he has only played 60 minutes. Now it is important that he recovers properly because he can be good for us and England.
"After so long out, I don't think it was easy for him before the game. But he worked well and scored a fantastic goal."