The former Everton man started his first game for the club since September during the champions' 2-0 win over the Blues at the Etihad Stadium.
Hart insists that Rodwell, who has endured an injury-hit debut season at City, will be given time at the club.
"It is nice to see Jack. I am really happy for him. He's a really good boy," Hart told ESPN.
"It's been hard for him, he's been injured a lot but when you get him fit you get good performances.
"Whatever Jack needs to do, whatever he needs, this club will give it to him. Be it fans or players, we're there for him because you know when you have got quality. Hopefully he'll get a little run of games together and we will see what he is about."
Rodwell joined City in the summer.