Hodgson has been criticised in the press this week following his appointment, and the FA also voiced their anger at a headline mocking the 64-year-old's speech impediment.
However, Bevington believes that Hodgson will carry on in a professional manner regardless of any criticism that comes his way.
Bevington told talkSPORT: "I think we had to make a stand as an organisation earlier in the week to show that there are certain things that we won't accept and that we want to stand by our man. We've got to set some markers down early in that respect, so that's what we have done.
"He's still enjoying the fact that he's been appointed as England manager and he's not been affected by [the bad press] in any way."