Barry was rested on Sunday in the victory against Sunderland after wearing the skipper's armband for England in the draw with Ghana the previous week.
Despite winning that honour the midfielder has been ridiculed by Joey Barton.
Barton derided the former Aston Villa player, describing him in a French football magazine as "a teacher's pet."
Mancini believes the Newcastle midfielder has little to shout about and said: "Joey Barton is a good player but Gareth Barry is a fantastic player. I can say only this. It is a situation that is not important to me."
On Rooney, he added: "" am disappointed because when we play a game like this it is important all the best players play."
Source: PA
Source: PA