The Gunners headed back into first place with a 1-0 victory at Newcastle, secured by Olivier Giroud's lone strike.
However, while Wenger is intent on remaining there, he admits it is too early to start thinking about the big prize.
He said: "Look, we believe in ourselves and we are determined to give our best, absolutely, and to turn back on the season at the end and think we have given our best.
"I hope it will be enough, of course, but it's a long way to go. It's too early to say that."
Arsenal had to scrap their way back above Manchester City in the table by winning a hard-fought encounter at St James' Park.
The Magpies went into the game having won seven of their last nine league games, and they threatened to take the lead in first-half injury time when first Moussa Sissoko forced a good save from Wojciech Szczesny before Mathieu Debuchy headed against the crossbar.
But Giroud proved to be the match-winner with a glancing 65th-minute header from Theo Walcott's free-kick after he briefly lost marker Mike Williamson.
The Frenchman passed up a glorious opportunity to seal the victory four minutes later and his side might have been made to paid when Szczesny blasted an 82nd-minute clearance straight at Loic Remy, but saw the ball run just wide.
However, Wenger was delighted with the resilience shown by his side, a trait he believes they have strengthened during the last calendar year.
He said: "We have come out of very difficult games - we have played Everton, we have played Manchester City, Chelsea, at West Ham and Newcastle.
"We have dropped some points, but I felt it was more down to the heavy schedule and the short recovery time we have had than to the difficulty of the games.
"But we have to show it on the pitch, and that's what we try to do."
- Sports & Recreation
- Olivier Giroud
- Wojciech Szczesny
- Manchester City