After Manchester United were beaten by Chelsea in midweek, victory for Arsenal would have put their title destiny in their own hands but they mustered few clear chances despite dominating possession and had to share the points with Sunderland for the second time this season.
Manchester City, who beat bottom club Wigan Athletic 1-0, are third on 53 and five clear of Chelsea who visit Blackpool on Monday.
Wenger was annoyed by two decisions that did not go his side's way, describing them as "absolutely disappointing and unacceptable.
"Unfortunately I've seen some things that are difficult to take but that's part of the game," he told Sky Sports.
"We have to take it on the chin and continue to fight. We had problems finding our fluency, I put it down to the quality of their defending and we missed some offensive players."
Birmingham City, who upset Arsenal to win the League Cup at Wembley six days ago, went down 3-1 at home to relegation rivals West Bromwich Albion and dropped into the bottom three.
West Ham United edged out of the drop zone with a 3-0 home win over Stoke City. Fulham beat Blackburn Rovers 3-2 thanks to a controversial late Bobby Zamora penalty and Ivan Klasnic also scored two minutes from time as Bolton Wanderers beat Aston Villa 3-2 to move above Liverpool into sixth place.
Everton beat Newcastle United 2-1 for their first league win at St James' Park in 11 years.
Sunderland's barren spell at Arsenal is more than double that, their last league win there coming in 1983, but they will be delighted to have gone home with a point.
With a Champions League trip to Barcelona and an FA Cup quarter-final away to Manchester United coming up next week Arsenal boss Arsene Wenger insisted his team were focused entirely on the job in hand but without injured trio Cesc Fabregas, Robin van Persie and Theo Walcott they lacked spark.
Andriy Arshavin had a goal ruled out for a dubious offside decision and substitute Marouane Chamakh headed against the bar 15 minutes from time but Sunderland went close to snatching an upset win when Danny Welbeck's fierce shot was well saved by Wojciech Szczesny.
Steve Bruce, Sunderland's manager and a veteran of many title run-ins with Manchester United, said Arsenal were feeling the pressure.
"We used to call it the 'tickly bit' when you get down to the last nine or 10 games," he told BBC radio Five. "That's upon them, there's a pressure and an edginess and what happened last week in the cup final doesn't help them."
Manchester City have played two games more than Chelsea and Spurs, their main rivals in the race for Champions League places, so needed to ensure a win over Wigan.
They were gifted their goal when keeper Ali Al Habsi allowed David Silva's tam
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