The Gunners host Chelsea on Saturday lunchtime aiming to recover quickly from a lacklustre 2-1 home defeat by Wigan on Monday night to keep themselves on track for automatic Champions League qualification.
Arsenal hold a five-point lead over rivals Tottenham and Newcastle heading into this weekend's fixtures, while they are seven in front of the Blues but having played a match more.
Just to be in this position is something of an achievement within itself, considering Arsenal's appalling start to the domestic campaign which saw them lose four from the first seven games and slip down as low as 17th.
However, the fact the Gunners are not now fighting for the championship itself will continue to rest uneasy with the Frenchman, whose side last lifted a trophy in 2005.
Wenger said: "We want more, but where we are at the moment we will be happy with third place because there are great teams who would be very happy if they got there.
"You always want more, but you see that the competition in England is difficult - Chelsea are now in the Champions League [semi-final] against Barcelona, but they are sixth at the moment, that means it is not easy.
"We want to win our next game and that is the only way we can secure our [Champions League] qualification.
"We have done remarkably well in the last two months and we want to take advantage of that run we have created and show that (on Saturday)."
Arsenal have won nine in the last 11 Premier League games to force themselves back into the top four.
Wenger feels ending the campaign with a similar run of form can only boost confidence for the challenges ahead in 2012/2013.
"We feel that as a team we have improved during the season and it is important now to finish in a strong way. That gives us confidence to do well at the start of next season," he said.
"We played the first seven games and lost four. It is difficult after to win the championship."
Chelsea beat Barcelona 1-0 on Wednesday night to take a slender lead into next week's second leg of their Champions League semi-final at the Nou Camp.
Wenger warned it would be a "massive mistake" to think the Blues will be distracted by their European exploits.
"We want to focus on our performance, let's not expect any lack of focus from Chelsea," he said.
"They are on a high so it is always natural to be up for the next game."
Wenger guided Arsenal to a famous 2-1 home win over Barcelona in Europe last season.
He added: "Chelsea were very good at what they did, they decided to defend and only to defend.
"When you choose the tactics they have chosen you have a 30% chance to win the game. They took their chances so you have to give them credit for the discipline they showed, for the consistency of their focus on what they wanted to do, and the fact that they could use the weakness of Barcelona on the counter-attack and set-pieces.
"The tie is a 50:50 now. If you don't concede at home and you win, in Europe that is always a good result because of the weight of the away goal."
While Chelsea may be on a crest of a wave under the guidance of caretaker-boss Roberto di Matteo, Wenger feels his men will be just as confident of producing a response from Monday night, when they were 2-0 down inside the opening 10 minutes.
"Like always after a big disappointment you focus on the next one, it is part of getting over defeats without losing your confidence," he said.
"You have to make sure that your frustration is transformed into energy in the next game."
Already without Jack Wilshere, Arsenal have seen their midfield options depleted further by the ankle injury to Mikel Arteta against Wigan.
On-loan Yossi Benayoun will not be able to face his parent club on Saturday, but Abou Diaby and Francis Coquelin return from injury.
Wenger said: "It is not ideal but we cannot complain, we have to overcome that.
"You always expect in April that not everybody will be on board and our game is based on collective play.
"That is why we have to focus on our team play and not think about who is here or not here."