Lampard, who played for Chelsea for 13 years, refused to celebrate after netting a late equaliser for his new side at the Etihad, but Redknapp, who is Lampard's cousin, thinks that his relative would have been pleased to grab his first City goal.
He told the Daily Mail: "Don't be fooled by the non-celebration. Frank Lampard will have been the happiest man in the dressing room after scoring that goal.
"He is the ultimate goalscoring machine and if he didn't want to score, what was he doing in the box? He will not have cared one bit about scoring against his old club.
"He has perfected the art of arriving late in the area and makes it look so easy. He's like a magnet to the ball but that's not down to luck — he has spent a lifetime [scoring those goals]."
Lampard will move to New York City FC in January.