Howard Wilkinson's young lions were very much second best to a lively Greek side, who intimidated their guests with their time wasting and niggly tactics.
Eventually, England lost their cool and after Tottenham's Luke Young saw red for a push, Chelsea defender John Terry was red-carded for a dreadful two-footed lunge on Vakouftsis.
England were outplayed for much of the contest and it took just 26 minutes for the home side to break the deadlock, when Papadopoulos crashed a header beyond West Ham keeper Stephen Bywater, who endured a torrid debut for the under-21's.
And they doubled their lead shortly before half time when the English defence were caught napping.
Young thought he had conceded a penalty for a late challenge inside the box, and with the defenders looking at the referee, Vakouftsis reacted quickly and slammed the ball beyond Bywater.
With England's hopes of qualifying in tatters, Wilkinson introduced Arsenal's Jermaine Pennant for the largely annonymous Jermain Defoe, but the change did little to improve a poor England display.
And their misery was confounded when Bywater, who endured an equally torrid league debut when he conceded five in West Ham's 5-4 defeat to Bradford last season, committed a glaring error, letting a soft John Terry back-header slip through his hands and roll over the line.
England restored some pride in the dying minutes when West Ham's Michael Carrick hammered a fine shot beyond Greece's substitute keeper Anastasopoulos, but things turned sour in injury time.
Young's shove sparked a mass brawl between the two sides, and once order was restored, Terry then saw red for his shocking late challenge.
Wilkinson was understandably disappointed with his side's display and their lack of discipline.
"Whatever the circumstances the players have got to learn to stay in control. They have been taught enough about it. It's vital you learn to keep in control," Wilkinson said.
"At this level they are told their behaviour level has got to be even more respectable than normal.
"Luke felt, whether it was accidental or not, that he had got a smack in the face and responded with a shove.
"John said he had got the ball and this was supported by other players but I pointed out that at this level more often than not that tackle is deemed to be reckless.
"They have got to learn. It is as simple as that."
