Former Three Lions captain reveals disappointment
Fifa's 22 executive committee members voted in favour of Russia's bid.
The former England captain, who was part of a 30-strong delegation who went to Zurich, helped deliver the county's bid presentation to Fifa with Prime Minister David Cameron and Prince William, and it was immediately applauded by Fifa president Sepp Blatter as "excellent and remarkable".
Speaking to Sky Sports News, Beckham said: "It's obviously disappointing coming away from Zurich without the 2018 World Cup but I think the whole bid team can be proud of what we put through and the presentation today was exceptional.
"Everyone we spoke to said it was one of the best if not the best presentation, but it wasn't meant to be.
"We send our congratulations to Russia and Qatar, they are two great countries and I'm sure they will do Fifa proud.
"At the end of the day, when you lose something you do feel that [injustice] and you do feel disappointed.
"It's more disappointment than anything right now. We'll process it over the next few days but the biggest thing is the disappointment.
"There's a lot of hard work gone behind the bid and a lot of belief in our country that we were going to get the World Cup.
"So obviously there's huge disappointment, but like I said, the bid team couldn't have done anymore.
"We got very got feelings from all the members that we met, and we met almost every one.
"Obviously it's disappointing to go out in the first round, it's disappointing not to get the 2018 World Cup but we send our congratulations to Russia and Qatar."
There has been speculation that the 'Panorama' programme on the BBC into allegations of corruption within Fifa, screened just three days before the vote, and the recent Sunday Times investigation into 'votes for sale' put a dent into England's bid.
Beckham said on that matter: "I don't know [how damaging the media allegations against Fifa have been].
"Ask the delegates that, because obviously I can't answer that question.
"I said during the week that our media has full support behind the bid and that hasn't changed."