The Premier League champions have been relatively quiet in this summer's window, which has sparked speculation that the Italian boss does not see eye to eye with football director Brian Marwood.
"Mancini won't be happy with not bringing players in," Summerbee told talkSPORT. "Every year the Premier League gets better and better, so you need to strengthen.
"It gives everyone a bit of a boost [by bringing in new players]. You want to keep improving every year, but it's still a top quality squad.
"I expected City to bring players in because they have done that in previous years. It would surprise me if nothing happens between now and the close of the window."
Former Everton midfielder Jack Rodwell is the only summer signing made by the North West club so far.