The Gunners showed plenty of grit as they battled back from two goals down to rescue a point in the closing minutes at Goodison Park on Saturday following a determined second-half showing.
Wenger compared the response of his players to the one they showed when the two sides last met on Merseyside in April.
Last season the north London club were also faced with a 2-0 half-time deficit at Goodison, but offered a tame showing after the interval as they went on to lose 3-0.
“When we got beaten here 3-0 it could have been many more,” Wenger said.
“Three was quite flattering on the day,” the veteran French boss added.
“For us to come back from 2-0 down against a team as good on the counter attack it shows the belief and resilience was there.
“It is our ambition (to challenge for the title). If we can maintain that, of course we can (be challengers).
“We had a big test and at half-time it was even a bigger test. We responded well. We were a bit nervous at the start. Before that we were a bit tentative and Everton are a good side as well.
“We gave a great response with a complete desire to come back and the spirit was fantastic.”
Wenger also played down concerns about the early season form of Alexis Sanchez after the Chile forward made little impact at Goodison and was replaced at half-time.
“At the moment he is not completely ready,” Wenger said.
“He knows he is not at his best physically but when he is his confidence will come back. It is always difficult to know why the confidence is not at its best.”
Everton had deserved their lead at the break, earned thanks to Seamus Coleman’s header from a Gareth Barry free-kick and Steven Naismith’s smart finish after great work by Romelu Lukaku.
But Arsenal pulled a goal back seven minutes from time when the impressive Aaron Ramsey slid in to guide the ball home from Santi Cazorla’s cross.
– Giroud worry –
France striker Olivier Giroud completed the comeback in the final minute of normal time with a powerful header from Nacho Monreal’s cross.
However, he limped off in injury time with an ankle problem, leaving Wenger hoping it was not a serious blow ahead of Wednesday’s second leg Champions League qualifier against Besiktas, where the tie is all square after a goalless draw in Turkey.
“It is a big game against Besiktas and I hope we have not lost him,” said Wenger of Giroud, who left the stadium with a protective boot on his left foot.
“In the final minute, he stretched his ankle.”
Everton manager Roberto Martinez said a lack of fitness had cost his side victory.
“The performance was phenomenal and it gave a clear direction of where we need to work,” he said.
“Scoring two goals should have been enough to control the game in a normal manner. But we dropped our energy levels and couldn’t contain the game like we normally do,” the Spaniard explained.
He added: “Every individual is at a different level. We have three players who arrived later from the World Cup. It was a very demanding game for certain positions.
“If it had finished 2-1 I think it would have been an incredible performance. The first-half display was as dominant as I have seen at Goodison against a top team.”
Naismith’s goal also met he has scored in consecutive matches for Everton having netted in their 2-2 draw with Leicester City on the opening day.
“It’s not just the goalscoring for Steven, his contribution is important,” Martinez said. “He is such an intelligent footballer, the way he wants to start games.
“He understands the game down to a tee, what is needed. I am delighted to see him score goals but even more by the way he is playing.”