The Gunners, who last won the Premier League in 2004 and have not lifted any silverware since landing the FA Cup the following year, went to the top of the table with a 2-0 home win over West Ham United on Saturday.
NEWS:Arsenal hit top spot
Arsenal also appear to have an easier run-in than title rivals Manchester United and Chelsea.
"My players have always believed (we can do it) and I believe we can as well," Wenger told the BBC.
"That is what champions believe - when no-one else believes you must believe you can do it. We have three teams involved in the fight, it is going to be interesting and we must win our games.
"But there is no room for error. The target is to win the next game and that is what we are going for. We do not think or speak about errors, we are just thinking about winning the next game," added the Frenchman.
Arsenal have won their last six league matches and most of their remaining seven fixtures look winnable too.
They face home games against Wolverhampton Wanderers, Manchester City and Fulham and trips to Birmingham City, arch-rivals Tottenham Hotspur, Wigan Athletic and Blackburn Rovers before the season ends on May 9.
The matches against Spurs and Manchester City, who are both challenging for fourth place, and Fulham, rejuvenated by manager Roy Hodgson, look the most problematic.
CHAMPIONS LEAGUE
Wenger's side also have to play holders Barcelona in the Champions League quarter-finals but those pundits who wrote off Arsenal's chances when they lost 3-0 at home to Chelsea in November to trail in the title race by 11 points, were wide of the mark.
"There is still everything to play for," Wenger told reporters. Arsenal were reduced to 10 men just before half time when defender Thomas Vermaelen was sent off for a foul on Guillermo Franco and although Wenger was furious with that decision, he was delighted with the way his team responded.
"We showed maturity today and kept our discipline and technically we were outstanding. Once again we showed mental strength and what we achieved today can only make us stronger," said Wenger.
Goals from Denilson and skipper Cesc Fabregas, with a late penalty, sealed victory and kept Arsenal, their fans and manager believing more success is just around the corner at last.
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