Speaking to Ryan Seacrest on his KIIS-FM morning show, the former England captain said that his whole family was content with the warm welcome they received in the US, "but on my side, it's frustrating at the moment."
Beckham said that he would try his best to regain fitness, but bemoaned that doctors were not sure about his speedy recovery.
"Obviously, I'll be working at trying to get myself fit and trying to get myself better, and hopefully be able to maybe play before the end of the season," People magazine quoted him as saying.
"But the doctors are not that sure about it. It's disappointing and frustrating at the moment," he added.
The superstar footballer strained his knee ligaments during a fierce tackle at Wednesday night's game against CF Pachuca Superliga at Home Depot Center in Los Angeles.
Although the team said that he would stay out of the game for as long as six weeks, Beckham reckoned that his recovery might take eight to 10 weeks.
"I'm hopping about at the moment, which isn't great," he said.
Beckham also believes that he committed a big mistake by not letting an ankle injury he had already been nursing heal properly, before getting back to the game.
"My ankle is not completely right, maybe 90 percent right. I always try to play. That's the problem. Coming back and going into game not fully fit, it gives my body a chance to have other injuries," he said.
He, however, admitted that his three sons had "reacted really well" to a new country and a new school.
"It's always difficult when you got three kids and trying to get them adjusted pretty quickly," he said.
"They love it here. We said it right from the word go: It's like they're moving to Disneyland. That's what they had in their heads straight away. They couldn't wait to get here. They've settled into the school," he added.
Beckham also revealed that he and Posh were planning to expand their family.
"At some point we will. We were speaking about it the other day. We both want four or five kids and a big family," he said.