The 25-year-old has been described as the world's best after a string of impressive displays for club and country.
But he has come under-fire recently with City leaking goals in the Premier League and Champions League, and also for England after an indifferent showing helped a Zlatan Ibrahimovic-inspired Sweden to a 4-2 win in midweek.
Mancini said: "For me he is the first choice but if he does not play well I change. I don't have any problem.
"Joe is like Mario Balotelli, like all the other players. For England I think it will be the same. If he does not play well maybe the manager can change the keeper.
"Costel Pantilimon is a good keeper and if Joe does not play well for five or six games, probably I can change the keeper. This is normal.
"But I trust totally in Joe, for me he is the best keeper in England. I am sure he can do some mistakes sometimes, this is a keeper's life.
"If a keeper does a mistake, you concede a goal and you lose. If the striker doesn't score a goal the game can finish 0-0.
"Ibrahimovic can score against every keeper. Ibrahimovic for me is one of the top five strikers in the world."