Bridge's ex-girlfriend has been at the centre of a media storm after an alleged affair with the defender's former Chelsea team-mate John Terry.
Carlos Tevez, Stephen Ireland and Nigel de Jong were wearing the T-shirts.
"The players are very close to Wayne," said Manchester City boss Roberto Mancini. "It was a nice gesture."
In a statement on Saturday, England international Bridge, 28, who missed the 2-0 win at Eastlands because of a knee injury, said he would not be commenting about the reports of the alleged affair.
"The reports deal with matters which are of a deeply personal and private nature," he said through his lawyers.
"My primary concern is the welfare of my son. Therefore, I intend to make no comment whatsoever either now or in the future about these reports and ask that my privacy is respected."
Mancini added: "He is a fantastic player and a good guy."
Source: BBC Sport
Source: BBC Sport