Hodgson stepped down as England boss after they suffered a humiliating 2-1 defeat to Iceland in the last 16 of Euro 2016.
The former Liverpool boss was out of football management for more than a year before being appointed as Frank de Boer's successor at Selhurst Park in September, after the Dutchman lasted just four Premier League games in charge.
When asked on 'Sky Sports' Sunday Supplement' whether Hodgson will feel he has a point to prove, Samuel said: "He says he doesn't, but he does because Roy is not without ego.
"Roy sees himself as one of Europe's foremost coaches. He worked at Inter Milan and he always used to tell you world rankings in international football meant nothing and then he would also tell you he got Switzerland to third in the world.
"I can understand that. He hasn't got a glittering playing career he can point to so this is all about him as a coach. You don't want to go out as a coach getting beaten 2-1 by Iceland.
"People say Harry Redknapp won't want to go out being sacked by Birmingham but I don't think Harry is as bothered by that sort of thing as Roy.
"I think Roy's reputation matters to him. Not in a way that he wants to put it before Crystal Palace - I think his priority is to keep Crystal Palace up - but at the same time I don't think the man wants to be remembered as the guy that got beat to Iceland.
"As we all know, that's how you become known as England manager. Steve McClaren won a league title in Holland but in this country he will always be remembered with his umbrella.
"In Roy's mind, if he keeps Palace up and does well at Palace that will count."