The Gunners headed back into first place after a 1-0 victory at Newcastle which was 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."
Opposite number Alan Pardew was disappointed for his players that their efforts had not been rewarded with a point, but was able to take some solace from their performance, and a return of 33 points from their 19 games to date.
He said: "It's not like I feel we have gone and reached something that's beyond us. I think 33 points is a fair reflection of how we have played, and we need to try to improve on that in the second half.
"I think we can. But the margins are so fine. It's not like we have come up against the top teams, played well and lost all of them.
"Obviously, we have beaten Chelsea, we have beaten Manchester United and they were as tight as today's affair.
"We have just come out the wrong side today, and if we can stay like that against the top teams all year, I will be relatively happy because I think we will win three or four of them."