The Gunners head to Goodison Park on the back of five straight Premier League wins which have catapulted them up into the top four.
Arsenal have come from behind in four of those games, the latest with a dramatic stoppage-time winner from Thomas Vermaelen to beat Newcastle 2-1 at Emirates Stadium last Monday night.
Wenger admits he would rather enjoy a comfortable win, but will take another crucial three points any way they come.
"Every time we were behind and every time we have shown outstanding spirit. It is not fantastic for your emotions, but overall when it finishes well you accept to suffer," Wenger told Arsenal Player.
"If that is the price we have to pay we are ready, but you just want to continue with the same attitude because I don't believe in luck too much on that side of the game.
"If you come back it is because you fight and if you fight you have a chance to come back. So let's fight first."
Wenger continued: "We are in a good, positive momentum. Now it is focusing on the next run to keep that going.
"That means playing with the quality we have played with recently and as well with the team attitude and spirit we have shown.
"I am sure that will get us the result."
Should results go their way this week, Arsenal could find themselves in third place ahead of the next round of fixtures, which see rivals Tottenham travel to Chelsea.
Wenger accepts there is little margin for error in the battle for Champions League qualification.
"It is so fragile that it is just down to the next performance. Therefore that is what you want to focus on," he said.
"We had a little bit of a breather because we could come out of the Newcastle game and not play for nine days basically so it is important for us to focus again and keep the momentum going."
Wenger added: "It is a key time. The fixtures are difficult for Arsenal, for Chelsea, for Tottenham.
"It will be about who does the best and who does the best will be the team who focuses on the next game, on the next result and on the next quality of the game.
"That is what we want to do of course, just focus on our next game and try to do as well as we can."
Everton have beaten Manchester City, Chelsea and Spurs at Goodison Park this year.
Wenger has been impressed by David Moyes' side.
He said: "They are a team who, when you look at the numbers, do not score many and do not concede many.
"They are dangerous on crosses, and they are a team that always has a good technical level overall.
"Everton are resilient, they keep going, they have a manager with experience and competence. Overall you can say they are one of the consistent teams in the Premier League.
"Nobody goes to Everton and thinks 'okay, it will be all right', everybody expects a tough opponent and that is what we will get."
Midfielder Mikel Arteta will return to Goodison for the first time since his summer transfer.
Wenger has been impressed by the way the Spanish midfielder has adapted quickly to a new club.
"He always gives you a certain level of quality, is always 100 per cent focused and committed, that is what you want from a real professional, and also he brings the best out of other players." Wenger said.