Wenger's men climbed to fifth with a 2-1 win at West Ham on Sunday and are involved in a fierce battle for the UEFA Champions League qualifying spots.
The Frenchman is confident Arsenal have the experience to see off the competition, with West Ham and Southampton also in the upper echelons currently, but was quick to highlight the long road ahead for his side.
"We have done it for 17 years, so we are entitled to the belief that we can do it," he said. "It's all to do because, when you look at the league, everyone is fighting very hard for it.
"Southampton, Tottenham, Manchester United, so many teams who can fight for these positions.
"I have always had that belief [that a top-four finish is possible] but it's far from done.
"We just want to win the next game and be consistent in our performances.
"We were just caught by Liverpool [2-2] in the last minute and [on Sunday] we won away from home.
"If you look at our recent results, we look to be more stable. We have a big game in front of us now against Southampton with nobody coming back.
"The players who played [on Sunday] have given their all and now we need to recover and prepare for the Southampton game."
Arsenal face Southampton in the Premier League on New Year's Day.
