His apology follows criticism from Saturday's referee Terje Hauge and even suggestions that he could be stripped of the England captaincy.
Hauge said he was surprised that the 29-year-old had deliberately fouled Ben Thatcher in order to be suspended.
Hauge told Standard Sport: "It is not correct to do that. He is the captain of the England team and he is a star.
"Many young players look up to him. It's not good for him to think and act like that.
"It surprises me if he has said that. In the match I didn't think he did that. I thought it was a reaction in the game.
"The situation was, for me, a very clear yellow card. I did not know he had a yellow from matches before.
"After the match I got information that it was the second yellow and he had to miss the next match."
Despite the apology, Beckham could still be censured by the football authorities for his admission.
FIFA president Sepp Blatter has said he wants the Football Association to take "adequate measures" against Beckham, who was back in Madrid today for a medical examination.
Blatter claimed the comments "hurt" him and wants FA chairman Geoff Thompson to investigate the matter and report back to FIFA.
He said: "It's not a matter for FIFA to speak about sanctions to a player of a national team.
"I have told my Mr Thompson that he should go into this matter and report it back to us.
"We are concerned at the attitude, the possibly bad attitude, of the player."
Eriksson has said he will deal with Beckham tomorrow, but he is understood to be angry at the way his skipper has behaved on the eve of what should have been a straightforward match.
