The Gunners head to Bolton on Wednesday six points behind Chelsea, who drew 1-1 at Swansea on Tuesday night.
Wenger was full of praise for the way his side rallied from trailing 2-0 at the break at home to Aston Villa on Sunday as they eventually ran out 3-2 winners to secure a place in the cup last 16.
The Arsenal manager expects another full-on performance at Bolton as his men aim to end a run of three straight league defeats.
"Our target is to show the response we showed against Aston Villa now in the Premier League," Wenger told Arsenal Media.
"We want to continue to chase up, to get up the league and fight for the top four."
Wenger continued: "We know from previous games that we have that strength and that the desire in the team is great. Overall the ingredients are there.
"We have the quality and I feel that if you look at results recently, we were very unfortunate because in every game we were in a position where we could win it.
"It is not that you felt there was absolutely no quality there, it is just that we missed what makes the difference a little bit, that was basically defensively because we had many defenders out.
"I believe that strength and belief again will allow us to transform our Premier League form positively."
Bolton may be struggling at the bottom end of the table, but Owen Coyle's side have picked up two wins from the last three league games, including a rousing 3-1 home victory over Liverpool.
Wenger is not expecting an easy ride at the Reebok Stadium.
"It will be a competitive game. No matter who you play in the Premier League, whether it is first or last, you have a competitive game," he said.
"If you don't really produce a top-class performance you don't win the game.
"Our target is to continue what we did against Aston Villa."
On transfer deadline day, Arsenal brought in attacking midfielder Thomas Eisfeld from Borussia Dortmund on a long-term contract.
The 19-year-old came through the German outfit's academy and leaves after seven years with the club.
Eisfeld has impressed for Dortmund's Under-19 side this season and has now completed a move to the north Londoners.
Andrey Arshavin was reported to have been offered the chance to return to Russia with big-spending Anzhi Makhachkala. The 30-year-old, signed from Zenit St Petersburg in January 2009, still has 18 months on his current contract left to run.
Japanese midfielder Ryo Miyaichi went on loan to Bolton until the end of the season.
The 19-year-old had a successful spell with Feyenoord last season, and returned to make two Carling Cup appearances for the Gunners.
However, under Premier League rules, Miyaichi will not be eligible to play against his parent club at the Reebok Stadium on Wednesday.
