Heskey said that it is not sensible to cling on to the slight hope that England can still get through, which would require Italy to beat both Costa Rica and Uruguay.
"I can't see it. It's out of our hands now," he told Goal.com. "We are clutching at straws. Costa Rica are capable of getting a draw, they looked lively in their first game, Joel Campbell in particular.
"It is a big surprise that England are in this position. Before the tournament, I thought we had enough to win the first game against Italy and get a draw with Uruguay. So it's major disappointment."
England's final group game is against Costa Rica on June 24.