The press claimed last week that Mancini had banished his striker from the club for three months after they clashed over the player's knee injury. But those stories were proved false on Sunday when he came off the bench in the goalless draw with Liverpool at Eastlands.
"They are both strong and opinionated and they are both winners,'' said Barry. "That is good for the club.
"We are working hard on the training pitch and all the players are right behind the manager.''
Barry accepts that the increased scrutiny on the club is part and parcel of their new-found status as big spenders.
"As a club we are in transition,'' he said. "We have spent a lot of money and we are looking to reach the top.
"But these things come with it. It was not even a row but it made the headlines. We come into training, looking to work hard. We see a headline and wonder why it is there. But all the top clubs have had it over the years.''
Mancini, meanwhile, hopes to have Carlos Tevez available again for Saturday's trip to Stamford Bridge. He has been back home in Argentina following the premature birth of his child.
"I don't know if Carlos has been doing any training over the last week,'' said Mancini. "I hope he has but I need to speak with him when he comes back.
"We play Wednesday but it is difficult to think he might play then. But for Saturday it is possible - and Saturday is more important.''