England lost 2-1 to Brazil in the World Cup quarter-finals on Friday and the England captain is now looking ahead to Euro 2004 in Portugal.
"That is next up on the agenda for us and it is something that I am convinced is well within our grasp," Beckham said.
"There is so much talent and desire in this squad that the 2006 World Cup in Germany has to be a genuine target for us as well."
Many people had been talking about England as possible World Cup winners before the game against Brazil and Beckham said he could see why.
Our spirit is unshakeable, our belief in each other is rock solid
David Beckham on England
"I honestly felt we would have won (the World Cup) in Japan if we had managed to get past Brazil," he said.
"That wasn't to be but there's always a next time. And who can dare say that we won't succeed in Portugal and Germany where we failed in Japan?"
The Manchester United midfielder said the spirit in the England camp had been excellent during the World Cup.
"Our spirit is unshakeable, our belief in each other is rock solid," he said.
"And it is not only on the pitch that we have that kind of attitude. We are all just as close off it.
"You only have to look at the way we all got on during this World Cup campaign to see that.
"We had a lot of young players in there alongside older, far more experienced ones who have been knocking around the international scene for years.
Aspects of my game were not right - my fitness wasn't what it usually is
"But the way everybody mixed could not have been more perfect."
Beckham admitted he had been below his imperious best in Japan.
"There were obviously aspects of my game that were not right. But I would not have gone into any game out there if I felt I was not capable of making a valid contribution.
"Obviously my fitness wasn't what it usually is but I still did as much as I could for the team.
"I scored our penalty winner against Argentina and then set up three more goals. So at the end of the day, I was pleased with my input."