He told Sky Sports: "I don't think it is a crisis, I thought the way we played today was not the level of a team in the bottom three.
"On the other hand it is six points from eight games and that is a very poor return.
"We need to start winning to climb the table and until we do the word 'crisis' will continue to be bandied around."
The new owners were in attendance at Everton, having already given their backing to Hodgson as the right man to turn around the situation.
"It is always nice to get a vote of confidence," said Hodgson.
"Whenever you lose a couple of games in a row these days your position is going to be questioned, so the new owners making it clear they thought I was the right man to do the job, you are always very happy to hear that."
He added with a smile: "Whether that has changed after today I don't know."
Reflecting on the match itself, Hodgson was satisfied with the effort of his players despite the disappointing scoreline.
He said: "We fell behind to a deflected block which fell kindly for Cahill so I thought at half-time we were a bit unlucky to be a goal down because we had got back into the game well.
"In the second half we did everything the team could possibly do, we played well, created chances, we limited them to very few and put them on the back foot."
Star striker Fernando Torres again drew a blank.
"I don't think he is physically unfit, I think he showed that today, he did plenty of work and we don't have any injury problems with him," said Hodgson.
"He got battered during the World Cup and mentally he is probably a bit low and he needs a goal or two to get it back. Certainly today I would have no qualms about his performance."