The Three Lions recorded their worst performance at a World Cup tournament since 1958 as they failed to win a game in being knocked out at the group stages.
Hodgson told reporters "I am in good company aren't I? I think you might be struggling very hard to come up with an [England manager] who wasn't in that situation. I certainly can't.
"Going out like we did in Brazil scars you. That will always be there but there is no point wallowing in the fact that you have received that scar.
"This is the first match of qualifying. We are not preparing for a World Cup final. We want to get off to a good start. We want to play well, we want to win but if we win 3-0 that still doesn't mean to say we're going to win the Euros in 2016."
England begin their Euro 2016 qualifying campaign against Switzerland on Monday in Basel.