Fabio Capello's side were one of the pre-tournament favourites after winning nine of their 10 qualifying matches.
But they seldom reproduced that form and had to settle for being group runners-up before being thrashed 4-1 by old rivals Germany in Bloemfontein yesterday.
And Heskey refused to blame the lengthy domestic season for England's under-achieving in South Africa.
The Aston Villa striker said: "We are disappointed to go out before the quarter-finals but it is back to the drawing board.
"We have come up against a very strong German side but we have got to go back and revaluate things.
"We have to look at certain stuff.
"But you can't blame the season in England for what happened. Germany played a long, hard season as well so you can't really use that as an excuse.
"The German league is just as tough as ours, even tougher some might say."