Sinclair signed for City from Swansea City last month.
Summerbee told the Manchester Evening News: "It's not the case that I think City have weakened, but he has to prove himself.
"He's come from a smaller club. It didn't happen for him at Chelsea, but he's proved himself away from there.
"I hope he brings the form he's shown already and do it at a bigger club.
"But Adam Johnson has proved himself for England and at crucial periods last season he was an important part of the squad.
"He set up goals, he scored goals. In my mind he's ahead of Sinclair. He's a better player, but I hope I'm proved wrong."