The 35-year-old central defender felt he was worthy of being chosen especially as Capello opted to include "a couple of half-fit players".
The Italian selected Rio Ferdinand and Ledley King, who had been struggling with injury, in his 23-man squad for the finals and persuaded Jamie Carragher to come out of international retirement.
Captain Ferdinand has since withdrawn with a knee problem, King is now undergoing treatment for a groin injury and Carragher looked short of pace when brought on as a half-time substitute in the opening 1-1 draw with the United States.
Campbell revived his career at Arsenal during the second half of last season after rejoining the Gunners on a short-term contract, which has now expired.
He told ESPN Soccernet: "I wouldn't mind being out in South Africa with the England team.
"The way I have been playing for Arsenal, don't you think I should be? I do. For sure.
"Regrets? You could say that. I regret the fact that the England camp didn't think of me. I would have put my heart and soul into playing for my country again.
"I played my heart out for Arsenal again and thought it was worthy of a chance with England. It never came.
"Surely, you pick people in the groove, and I was back in the groove, and I was fit.
"Instead, Capello picked a couple of half-fit players. It fell right for them. Not for me."
Campbell added: "I can understand if Capello was thinking 'this guy is for England's past' but then he went back for a couple of players who had retired from international football.
"That I couldn't understand if he wasn't interested in going back to me.
"Not only that, Capello has gone for one centre half who didn't have a very good season, and another who just missed out on relegation.
"It's crazy when you think about it, that I would have done anything for crack at it, but never did.
"I was really, really hurt to be totally overlooked without even having an opportunity.
"I have been playing with England teams since I was 15 years old. I have won 74 England caps - been there, got the T-shirt - and it's experience that counts at this level as well."