Capello included Glen Johnson, Phil Jones and Kyle Walker as his right-back options for friendlies against Spain and Sweden, which take place on November 12 and 15 respectively. Chris Smalling, currently injured, was unavailable for selection.
The England coach's squad announcement was met with dismay from QPR midfielder Barton, who has links to both Manchester City and Newcastle. Reacting on Twitter, Barton questioned how some of his former colleagues could possibly be overlooked.
"Don't understand Eng Squad," tweeted Barton. "No Newcastle players?? No Micah Richards?? Surely he has to be. Man City 5 pts clear, MoM (man of the match) at Old T (Old Trafford) and skipper??"
Richards has only featured once for Capello during the Italian's England reign, but he is arguably performing better now than at any other moment during that period. The 23-year-old confessed his initial disappointment with the exclusion on Sunday, but now he is vowing to force his way into the international setup.
"I must be doing something right," Richards said. "In seasons gone by I have not been playing my best. Now I've started off well and we are top of the league.
"As I've said before, it's up to Capello. If he wants to give me a shout I am always there. I have improved, twice, three times since the first time I played for England.
"We have got a fantastic manager (Roberto Mancini) who has helped me so much. Even by giving me the captain's armband, it boosts my confidence. He just tells me to go out, enjoy it and express myself.
"I've still not been given a start under this England manager, so I've not been able to show what I can do. I know my form has to be right for City before he can pick me, but if he gives me my chance I am sure I can take it with both hands, just like I did before.
"Jones and Smalling have been doing well for Manchester United. If the manager wants to give them a chance it is up to him, there is no point in me moaning about it. I know what I've got to do - keep working hard - and that's what I'll do."