Arsenal boss Wenger accepts third-place finish
Nicklas Bendtner's second-half header eventually secured a 14th home league win and an unbeaten campaign at Ashburton Grove.
"The fluency was a bit difficult sometimes and you could see that it was a bit of an end-of-season game," said Wenger. "Everton did not open up at all, but we were controlled as the back.
"We did not create as many chances as usual, but scored a great goal and just about deserved the win today."
"We can still finish second if Chelsea loses one game and draws another one," said Wenger, "but Bolton are safe and having seen West Ham against Manchester United yesterday, I have very little hope Bolton will make a result at Chelsea."
Everton, meanwhile, still need a result from their final match of the season at home to Newcastle to make sure of fifth place ahead of Aston Villa which would secure qualification for the UEFA Cup again.
David Moyes was somewhat frustrated that result had not come in this game.
"I thought we were unfortunate," he said. "I am disappointed we didn't get a point we needed because we did enough to get it.
"Arsenal did not have many chances and we played well defensively."
The Everton boss, though, was glad to have destiny in their own hands.
"Three points ahead with a game to go is a position I'm happy to be in," he said. "I am confident the players can do it."
Moyes added: "For long periods we got closer to the top four, for eight months of the season.
"But the clubs above us are used to the last couple of furlongs and we found it tough.
"But saying that we qualified for the Champions League with 61 points a couple years ago and we have got 62 now. Maybe the Premier League has got better. Whatever happens next week we already have more points than we ever have before in the Premier League.
"That battle just underneath the top four teams has been tough. We have to try and do it again. We enjoyed Europe so much this year. Let's hope we can do it."