The 30-year-old midfielder, who has overcome three years of injuries to make his comeback, hit the first goal of the third-round tie in a man-of-the-match performance that lasted almost an hour.
Mancini fielded a completely different team to that held 2-2 at Fulham and gave the armband to defender Kolo Toure in his first game back after a six-month suspension for taking a banned diet pill.
The City boss said: “I am very happy for Owen, for Kolo and for the team. Owen is a fantastic player and he can become an important player for us. He can play often.
“He had no problems tonight. He’s had no problems for the last two weeks. We said that he would have about 60 minutes before the game, and I’m happy for him.
“It’s important that he becomes again the player that he was, then he will be important to the England team as well.
He played well, moved well and scored a fantastic goal
Champions League winner Hargreaves was omitted from City’s squad for the group stages, and Mancini said: “We didn’t know four weeks ago what his condition would be. In January maybe it’s possible that he will go on the list.”
Toure, who lost the captaincy to Carlos Tevez last season, cleared off the line in Birmingham’s only threatening moment and earned an ovation at the end from a 25,070 Etihad crowd.
He said: “I just want to thank the boss for giving me the honour of being the captain tonight. The fans were behind me and I want to thank all the people who have supported me in a really hard time.
“I’m back doing what I love and I will enjoy it. I’ve been working really hard - I had only one week rest, because for me it was important to come back really strong. It’s been a nice night for me.”
