The Three Lions fell to defeat against Uruguay in Sao Paulo thanks to a brace from Luis Suarez, and Costa Rica's surprise win over Italy made sure that Steven Gerrard and company would be making an early exit from the competition.
However, Heskey feels that Hodgson has earned a reprieve, for now, while he brings through fresh blood.
He told Sony One Stadium: "I think he should be spared until the next tournament to really push a new generation of players coming through. You can't keep changing the manager after every tournament.
"Who else is there? There are no obvious candidates among the English managers.
"I enjoyed playing under foreign managers but believe it is the right call to promote English talent for England. I think we should be grooming the best young English coaches for the future."
Hodgson will be 68 when the 2016 European Championships take place in France.