The Gunners missed a host of chances against a staunch Toffees defence at the Emirates Stadium which saw the Gunners go just two points clear of fourth-placed Chelsea (who have two games in hand) and fifth-placed Tottenham (one game extra to play).
Despite that, Wenger is remaining positive that his side can get the job done as long as they focus on what is happening in their own backyard.
"We are in a strong position still, but let's win the next game," Wenger told Sky Sports.
"We can only take care of our results.
"I think we are on a very strong run and as you could see we are ready for a fight, if we keep this fighting spirit, which we will, I am sure we will get there."
On the game, Wenger added: "It was a game of high intensity with unbelievable fight, but in the end I think we had chances to win the game.
"I am proud of the effort we put in and fantastic focus we have shown for 90 minutes, but just a bit disappointed we couldn't take our chances."