Arsenal was looking to move level to go fourth in the Premier League by overcoming a Burnley team that had lost its last two away games 3-1.
However, the Clarets held firm at Emirates Stadium on Sunday, with Nick Pope making some fine saves and Alexandre Lacazette spurning a glorious opportunity.
It means Arsenal head into the Premier League's winter break sitting in sixth, while Burnley are bottom but hold between two and four games in hand on their relegation rivals.
The Gunners had 20 attempts, with five hitting the target, yet they have now failed to score in four successive matches in all competitions. It is the first time they have gone on such a run since December 2005.
Arsenal has also failed to win any of its first five games in a calendar year for the first time in 27 years, while it is the first time since October 2008 that they have not beaten a team at the bottom of the league at home.
"We started slow, we looked leggy and didn't have enough rhythm or intention to attack the way we wanted," Arteta said.
"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."
For all their possession (75.7 per cent), Arsenal only created one big chance against Burnley, defined by Opta as an opportunity from which a player would be expected to score, though they finished with an expected goals (xG) of 1.4, suggesting their finishing was below par.
Pope made two excellent saves to deny Martin Odegaard and Emile Smith Rowe, who subsequently turned provider for Arsenal's best chance, only for Lacazette to prod wide of an open goal from the midfielder's cut back.
With Pierre-Emerick Aubameyang's future uncertain – albeit he was unavailable for health reasons on Sunday – Arsenal are reportedly keen to bring in a striker this month, and it would seem it is a vital need if they are to secure Champions League qualification.
Dusan Vlahovic is said to be a target, with Fiorentina willing to sell the forward, who scored 33 goals in Serie A in 2021, matching Cristiano Ronaldo's record from 2020. However, the Viola have insisted no offer has yet been received for a player rumoured to be valued at €70million (£58.6m).
Everton's Dominic Calvert-Lewin has also been linked, while Arteta has previously said he would like to bolster his midfield, but asked about Arsenal's transfer plans for the remainder of January, he replied: "In this market things are complicated."
Burnley did offer a threat of their own, with Dwight McNeil particularly dangerous on the counter. No player had more than his four attempts, one of which almost caught Arsenal goalkeeper Aaron Ramsdale cold early on.
Ramsdale did his part, however, and that was the only save he had to make. The former Sheffield United goalkeeper echoed Arteta's complaints about Arsenal's attacking output.
"I will give credit to Burnley, we know what they are about, it is frustrating from our behalf because we were putting balls into the box and that's meat and drink for Burnley," he told BBC Sport. "We didn't create that quality we needed."
Ramsdale was not wrong. Arsenal played 42 passes/crosses into the box – a season-high for the Gunners. Indeed, their 23 crosses from open play was also a high mark for 2021-22, yet only two of these were successful.
Battling Burnley made 42 clearances, including 27 headed clearances. Both figures are season-highs for Sean Dyche's side.