Sean Dyche hails Burnley's best all round display of the campaign
and live on Freeview channel 276
The Clarets kept a ninth Premier League clean sheet of the campaign against the Gunners, the most in the division alongside Sheffield United and leaders Liverpool.
Pierre-Emerick Aubameyang went within a whisker of giving the visitors the lead with a second half header, but it was the hosts who went closest to taking maximum points.
Ashley Westwood's delivery was helped on by Dwight McNeil and Jay Rodriguez, with the goal at his mercy, guided the ball on to the underside of the crossbar before it dropped onto the line.
Goal-line technology confirmed that the ball was just milimetres away from crossing the line and referee Chris Kavanagh awarded a corner after defender Shkodran Mustafi cleared.
"I agree with that," said Dyche. "In the balance of the game we defended well as you have to of course because it is the Premier League.
"The tactical set-up I was pleased with and how we delivered that. We were effective with the ball and asked enough questions by varying the play which I like and I like mixed football.
"I like to ask as many questions of the opposition as we can and I thought we did that. The only thing missing was a goal."
It was a seventh point from three games for Burnley, who had beaten both Leicester City and Manchester United beforehand.
The point moved them up to 11th in the top flight, level on points with Mikel Arteta's men, Newcastle united and Southampton.
Dyche said: "I think when you play like that against a good side like they are then of course you come away thinking was that the one we should have won?
"But in balance to that it is another clean sheet, another good performance ad after a tough run to get seven from the three games is a very good marker.
"It shows the players are ready for the challenge and that is important. The performance today was a very strong one."