Beckham, who lifted the side's tempo following his second-half introduction and hit the post, is eager to retain his place in Fabio Capello's squad and revealed that one of the key factors in that plan - agreeing a second loan spell with AC Milan - is "95% done".
Speaking after two goals from Peter Crouch and one from Shaun Wright-Phillips sealed victory in their final Group 6 outing, the Los Angeles Galaxy midfielder said: "Tonight was important for getting over the loss [against Ukraine on Saturday].
"We needed to end on a high. We didn't deserve to lose last time and we wanted to end the campaign well.
"We all have to prove with every game and every training session that we want to be in the squad for every game," said Beckham. "Not just the World Cup, but every qualifier and every time we meet up."
On his likely return to the San Siro, he added: "It's close. I've always said I want to go back there if they want me. AC have said they wanted me back since I left to go back to the United States and they're saying the same now.
"It's 95% done, so I don't know why it wouldn't happen now."