Arsenal thought they should have had a penalty in the final 15 minutes when Erik Pieters appeared to handle in the area but referee Andre Marriner did not give it and his decision was ratified by Kevin Friend, the VAR.
"I think it's obvious and clear, I think there is no debate about that. If that is not a penalty, then would someone explain what a penalty is in this league," Arteta told reporters after the game.
There was further drama in the final six minutes when Pieters was then sent off for handling Nicolas Pepe's goalbound effort and a penalty was awarded, only for the red card to be rescinded and the penalty withdrawn following another VAR review that showed Pieters had used his shoulder.
The draw means Arsenal failed to make progress in their attempt to finish in the top four, with Arteta's side nine points off Chelsea in fourth.
Burnley manager Sean Dyche said the VAR decision was an example of the value of the system.
"That is what VAR is for, those exact moments. That is when it [VAR] is worth its weight in gold because it clearly hits him on the shoulder," he said.
"The only thing I would say about the referee is that he couldn't wait to get the red card and I don't know why that is. Just take a moment and absorb it and then make a decision, in my opinion."
Arteta made five changes to his side ahead of a trip to Greece to play Olympiakos in the Europa League next Thursday before the North London derby with Tottenham next Sunday. And his side got off to the perfect start when Willian found Aubameyang early on, and his low shot squirmed past Nick Pope and into the bottom corner to put the visitors ahead. Pope would not have wanted to see a replay of that one, especially with England manager Gareth Southgate in attendance ahead of the upcoming international break.
Burnley, looking to complete a first league double over Arsenal since 1963, were flat in the first half and should have fallen further behind mid-way through when Bukayo Saka, on his 50th league appearance for Arsenal, sent a gilt-edged opportunity wide from close range.
Dyche's men had played twice since Arsenal's win at Leicester last time out for Arteta's men and it showed, with the home side looking lethargic against an energised visiting attack. Thomas Partey was the next player to threaten a shaky Pope but his effort sailed over.
The home side needed a moment of fortune to get back into the match and it duly arrived seven minutes before the break in comical style. Xhaka received a pass from Bernd Leno and looked to find David Luiz, but his ball was weak and cannoned off Wood into an empty net to give Burnley the most unlikely of equalisers.
Martin Odegaard tested Pope with a low drive six minutes into the second half as Arsenal sought to regain their lead, before Saka had an effort blocked inside the area. Arteta then introduced Alexandre Lacazette for Martin Odegaard just after the hour mark in a bid to spark his side into life, and his side were certain they should have had a penalty when Pieters appeared to handle inside the box.
Chris Wood wasted a glorious chance to put Burnley ahead with 10 minutes remaining but Leno stood firm to deny him and at the other end, substitute Pepe fluffed his lines with the goal at his mercy.
In a dramatic finale, Burnley survived two calls for penalties and Arsenal hit the post through Dani Ceballos as the home side clung on.