Liverpool defender Carragher was brought out of international retirement to take up a place in Capello's World Cup squad and made two appearances in South Africa.
He missed the vital win over Slovenia through suspension and was unable to reclaim his spot in the team for the disastrous 4-1 defeat by Germany which sent England crashing out at the last 16 stage.
Carragher was delighted to be involved in the tournament, but the 32-year-old has confirmed he is not planning to be available for national team duty next season.
"This was a one-off thing," he said. "The manager said he had a few injuries and I came into the squad and helped.
"I was delighted with the opportunity to play in a World Cup and work with Capello, but I have always said the most important thing for me is Liverpool Football Club."
England's early demise in South Africa led to calls for Capello to be replaced as coach, but the Football Association has given its backing to the Italian - a decision which finds favour with Carragher.
He added: "Obviously I wasn't involved in the qualifying stages, but that went great. The World Cup hasn't gone as well - so maybe I'm the problem, not Capello!
"Bobby Robson went out on a high in 1990, but a few tournaments didn't go too well for him.
"That's part of the game and I am sure with the experience of this tournament, hopefully the lads will get to the next one and be a lot better for it.
"I don't think there are many managers out there with the record he has got. I think with that itself he certainly deserves another crack at the England job."
Carragher admits England were poor, but has rubbished suggestions that there were divisions within the camp during their time in South Africa.
He continued: "I have not been in the squad for a while so it was new to me in terms of the manager and different things.
"But I do think with England when things don't go well people are always looking for things.
"People are looking for different reasons why it went wrong, but the bottom line is we just didn't perform well as a football team rather than anything else."