The Hornets, whose immediate return to the Championship was confirmed last weekend, were thrashed 5-1 by Leicester in their final home game of the campaign.
Goalkeeper Ben Foster claimed after Sunday's humiliation that “no manager in the world" could have kept the club in the top-flight.
Hodgson, who is Watford's third coach this term following the sackings of Xisco Munoz and Claudio Ranieri, revealed there has been division within the camp but refused to fully point the finger at underperforming players.
“A football club is an amalgam of many things. Players, of course, are the most important in a way, after the ownership and the people who make decisions at the top. And the manager comes somewhere in that amalgam.
“I wouldn't like to blame it totally on the players, no. I think that probably the reason for failure perhaps needs to be analysed a bit more closely, in a bit more depth. But I understand what Ben is saying.
“It is, to some extent, the feeling amongst a certain group of the players that they haven't had enough support from some of the others.
“So I understand that Ben, who is an honest guy, feels that it was important to make that point.
“I can only say I understand what he's saying or where he's coming from. But I'm not prepared to say it myself."
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