The England international was handed a straight red for his tackle on Seattle Sounders midfielder Peter Vagenas in the 17th minute of the clash that ended 2-0 to Seattle.
Beckham said he meant no harm with his challenge and believed the decision to be sent off was a slightly harsh.
“Pete is one of my best friends,” he told the club’s official website.
“I think it’s a hard tackle but not with means for a red card.
“I’ve never gone in one tackle wanting to hurt someone. The referee saw it differently.”