Hodgson watched on as his side went down 2-1 to Uruguay in Sao Paulo on Thursday, a defeat that left England's qualification hopes in the balance.
Elimination was then confirmed on Friday when Group D rivals Costa Rica beat Italy 1-0, meaning England failed to reach the second round of the tournament for the first time since 1958.
But Heskey, part of the squad for both the 2002 and 2010 finals, believes Hodgson is the right man to take England forward.
"I think he should be spared until the next tournament to really push a new generation of players coming through," he told the Sony One Stadium website.
"You can't keep changing the manager after every tournament.
"Who is else 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."
Despite voicing his support for Hodgson, Heskey believes that England got their gameplan wrong during the defeats to Italy and Uruguay.
"The tactics were not right," he added. "We defended badly, we did not get close enough to them in defence.
"(Mario) Balotelli running off the back of the defender, (Luis) Suarez, running off the back of the defender were examples of this. It meant the centre-halves were exposed because the full-backs were out of position.
"England played at too fast a pace. Too many players were out of position, in particular against Italy with (Wayne) Rooney on the left. (Raheem) Sterling could have played there.
"I think (Daniel) Sturridge merited playing as a centre-forward but I would probably would have played another player rather than (Danny) Welbeck out of position."
