Hodgson made nine changes to his line-up, with eight players rested and one enforced through injury, as he instead focused on arguably the most important game in the club's history on Thursday.
With the second leg of their Europa League semi-final at home to Hamburg in mind, Paul Konchesky, Aaron Hughes, Danny Murphy, Brede Hangeland, Dickson Etuhu, Damien Duff, Zoltan Gera and Simon Davies were all left at home.
To Fulham's credit, they came within seconds of claiming a point, only to be denied by a contentious penalty from Mikel Arteta with what was virtually the last kick of the game in a 2-1 loss.
"After the performance we gave, against a very strong Everton team, I would be absolutely amazed if people have the temerity to discuss our team selection," said Hodgson.
"We're going into very dangerous ground when the Premier League decides whether teams are strong or not.
"Hull made six changes to their team (against Sunderland) because they chose to change six players.
"So I should also be entitled to change players when I want to, especially given the situation we find ourselves in.
"I am not at all convinced that if the same 11 players who were in Hamburg had played against Everton we would have given as good an account of ourselves as we did.
"Do I think we have a case to answer in terms of letting down the Premier League, in terms of having favoured opponents by possibly fielding a weaker team?
"I can stand here quite happily knowing we certainly haven't done that. Quite the reverse I would think.
"We should be congratulated by all the teams around us for fielding the team we did, for having the courage to do it, because this team pushed Everton to the limit, and not many teams have done that to them at Goodison Park this season."