Aaron Ramsdale suggested Arsenal played into Burnley's hands by going too direct
(Image: BT Sport)
They have also failed to score since their first-half opener against Manchester City on New Year’s Day, a performance they have failed to replicate since.
Sean Dyche’s men set up with a typically low-block and had Nick Pope to thank after making saves from Emile Smith Rowe and Martin Odegaard.
Alexandre Lacazette spurned the best of chances however, screwing his shot wide after a smart Smith Rowe centre.
But despite creating chances, Ramsdale caimed their direct approach made it easier for their opponents.
He told BBC Match of the Day: "I will give credit to Burnley, we know what they are about, it is frustrating on our behalf because we were putting balls into the box and that's meat and drink for Burnley.
"We didn't create that quality we needed. We are at the moment depleted and the lads have played a lot of minutes, I don't want to make any excuses. We have time to regroup now."
Meanwhile, Arteta said his side looked “leggy” following Thursday’s defeat to Liverpool, failing to show any kind of rhythm in yet another blank.
"We started slow, we looked leggy and didn't have enough rhythm or intention to attack the way we wanted,” the Spaniard explained. “We started to play better, more rhythm and threat and came out in the second half completely different.
Mikel Arteta watched Arsenal go without a victory in all competitions in the month of January
"We tried in every different way but lacked the quality in the final third. At the end, when we have a really low block, you need spark and creativity to win football matches and today we didn't do that.
"It is what they do, they want to play a slow game, it is their game and you have to respect that.”
Arsenal now have a lengthy break before their next match, when they take on fellow top six hopefuls Wolves at Molineux.
The first-team squad are now set to fly out to Dubai for a warm weather training camp to rest up their bodies for the start of the run-in next month.