The Football Association's board voted unanimously to sack the former Middlesbrough boss on Thursday morning after the Three Lions' disastrous failure to reach Euro 2008.
Beckham, 32, came on as a half-time substitute in last night's 3-2 defeat to Croatia which sealed England's fate, and he believes the FA will have few domestic candidates to contemplate when it comes to appointing McClaren's successor.
Beckham told Virgin Radio: "There are not many English managers out there that haven't got jobs already.
"There are also a lot of talented foreign managers."
The Los Angeles Galaxy midfielder also insisted that McClaren retained the backing of the dressing room for the duration of his reign.
"The support was there for the manager last week," Beckham said. "And rightly so because players support managers and support people that they believe in.
"Obviously Steve is not the England manager anymore and everyone has to come to terms with that."
Beckham reiterated his determination not to retire from international football after Wednesday night's disappointment at Wembley, and even claimed he could still be around if England bounce back to qualify for the World Cup in 2010.
The former Manchester United and Real Madrid player, who won his 99th cap last night, insisted: "I said at the start of my career I'll always want to play for my country and I'd never retire from playing for my country.
"That could obviously be taken out of my hands but I want to reach my 100 caps. To get those 100 caps would be a dream come true for me."
Of his chances of featuring in 2010, Beckham added: "I'll still be available.
"Hopefully I'll still be playing, and playing well enough to be in the England squad in 2010.
"But who knows? Everything can change, and I have seen that in the last 12 months."