Beckham announced his retirement last week.
McClaren dropped Beckham as England manager, but said: "David forced himself back into the reckoning by his application and determination. I have no regrets about the decision I made about leaving him out but I was glad to be able to bring him back.
"'I just felt that with David making a commitment to play in America for LA Galaxy it would be difficult for him to continue in the team, although I always left the door open for his return. There were younger players coming through and I regarded it as an opportunity to make a statement regarding the old guard and bring on the new ones."