Tottenham ace Parker, 31, found it tough going against France in Donetsk on Monday and eventually had to be substituted.
Liverpool's Gerrard lasted the entire 90 minutes but, at 32, his stamina cannot be taken for granted either.
It is something Hodgson will have in his mind as he selects a team for Friday's Group D encounter with Sweden in Kiev.
"But I'm sure I'm not going to be the only coach wondering 'can they do it every four days?' about their players. That is what tournament football is about.
"What we've got to make certain of, is that if they can't, or start to show signs of fatigue, that others are ready to go in and do exactly the same job."