Theo Walcott gave the Gunners the perfect start, with his deflected strike looping beyond Tim Howard and into the top corner after just 50 seconds.
However, Marouane Fellaini capitalised on a sloppy pass by Bacary Sagna to drill the Toffees level midway through the first half.
Both teams had chances to win the game after the break, with the Toffees left aggrieved when they were denied a penalty following a challenge by Mikel Arteta on Steven Pienaar.
"You have to give credit to both teams who gave absolutely everything," said Wenger. "It was tense, uncertain and with total commitment on both sides.
"I hope we will recover in time for Saturday as we have now had three very physical games.
"My players have given a lot; it was a fair point for both sides. I'm happy with the commitment and desire, overall it is encouraging."
Wenger also praised winger Walcott, who made a goalscoring return to the team after recovering from a shoulder injury.
"Theo was fit again and scored a great goal," said the Frenchman. "He was not completely himself in the second half as he had a problem with his ankle at half-time, but he was very efficient and dangerous."
Asked whether Everton should have had a penalty for Arteta's challenge on Pienaar, he added: "To me it didn't look like a penalty at all."