It put the Merseysiders within one point of their fourth-placed opponents with a match in hand at home to Crystal Palace, placing Arsenal's chances of a 17th successive season in Europe's elite club competition in serious jeopardy.
"I am absolutely 100% determined to fight to make the top four but it will be difficult," said Wenger.
"We have still a programme that is feasible but we have to first focus on the quality of our performances before we dream of places.
"Let's get back to playing better than that. Our performance was not convincing, not defensively, not offensively.
"We had a lot of the ball and were not really dangerous. At the moment we lack a bit of confidence to be dangerous and lack penetration as well.
"You feel from outside that the penetration and incisiveness of our games is missing.
"Everton were better and deserved to win. It was a very disappointing result and a very disappointing performance.
"We have to regroup and get back to basics.
"The fight is very open and is depending not only on us. Everton are in a strong position but we have confronted that before and it is how we respond."
Wenger was asked whether fear was gripping his side as their previously unchallenged place in the top four came under threat.
"I don't know. It is very difficult to identify that it is fear," he added.
"Our big team defeats away from home have taken something of our charisma from the team. Is that belief? Is it fear? Is it confidence?
"I wouldn't question the spirit of this team. They are focused and want to do well but they have lost something on the confidence front."
Everton manager Roberto Martinez won the tactical battle as his side played Arsenal off the park to register their sixth consecutive league win, equalling a club record dating back to November 2002.
"The work-rate and discipline in a group sport was as good as it gets," said the Spaniard.
"Playing a top-four team at this stage of season we have never had this demand, so I can't compare the performance to another.
"The implications today were quite unique. We were hoping for a result but what was needed today was breaking many barriers.
"In 22 games we have played against Arsenal we only scored one goal or less: today we kept a clean sheet and scored three and looked like we could have scored more.
"The performance had an arrogant focus which was very pleasing to see."
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