Arsenal still look a level below Chelsea and Manchester City, but Wenger insists it is not unreasonable to think his team could win the Barclays Premier League this season.
"That is our ambition," he said.
"We had a big test today and at half-time it was even a bigger test. We responded well. If we can maintain that, of course (we can win it)."
Wenger was right when he noted Naismith was marginally offside when he converted Romelu Lukaku’s pass to put Everton 2-0 up.
It was a brilliant counter-attack move which showed just how clinical and expansive Everton have become under Roberto Martinez.
The way in which Coleman leapt to head home Gareth Barry’s chipped cross also pleased the Spaniard, who hailed his team’s performance as "phenomenal".
But the Everton boss could not hide his dismay at the way sloppy marking allowed Ramsey to turn home Santi Cazorla’s cross, then poor defending permitted Giroud to head in Nacho Monreal’s ball into the box.
"For 70-75 minutes it was the perfect performance, very similar to the one we had last time against Arsenal," Martinez said.
"The first half was full of dynamic football. Scoring two goals should be enough to control the game in a manner we normally do.
"Certain individuals, and as a team, dropped our level. The disappointment is the result but the performance was phenomenal."
Martinez was worried to see his team tire in the dying minutes.
"There was a drop in our energy levels," the former Wigan boss said.
"We are not a defensive side. We want to get on the ball but to do that you have to have the energy to do that.
"The energy levels at the moment are vital for us to perform for 90 minutes."