The Gunners failed to break down a resolute Everton defence at the Emirates with the draw not doing either side much good in their battle to qualify for next season's UEFA Champions League.
The draw leaves Arsenal two points clear of fourth-placed Chelsea and fifth-placed Tottenham, but having played two games more than the Blues and one more than their bitter rivals Spurs.
However, Wenger is confident they can get one of the coveted top four spots if they show the same fighting spirit they displayed against Everton.
"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."
Wenger was unhappy with some of referee Neil Swarbrick's decision-making, feeling he let Everton get away with some over-zealous tackling.
"I felt that the referee let a lot through on their side in the first half, but we adapted well and we responded very well physically and overall we kept a clean sheet - that was the target - and we wanted to score goals.
"We had the chances to score, maybe we looked too much for power and not enough just to place the ball."
Asked if Darron Gibson should have been sent off in the first half after escaping a second booking for a foul on Theo Walcott, Wenger replied: "Could have done."
Wenger was proud of his side's performance, but disappointed they could not take all three points, feeling they created the better of the chances in the 90 minutes.
"It was a game of high intensity with unbelievalble fight, but in the end I think we had chances to win the game," continued Wenger.
"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."