The Arsenal manager criticised the decision to overturn a penalty awarded after substitute Eberechi Eze went down in the box under pressure from defender David Hancko late in the match.
Referee Danny Makkelie initially pointed to the spot, but reversed his decision after a VAR review, sparking furious reactions from the Arsenal bench.
"What I am incredibly fuming with is how the penalty on Eze gets overturned in the manner that it happened," Arteta said after the game.
"This changes the course of the game at this level. I am sorry, but this cannot happen."
Arsenal had earlier taken the lead through Viktor Gyokeres, who converted from the penalty spot after Hancko fouled him inside the area late in the first half. The striker calmly beat Jan Oblak to register his 19th goal of the season.
Atletico responded strongly after the break and levelled when Julian Alvarez scored from the spot after Arsenal defender Ben White was penalised for handball following another VAR intervention.
Arteta accepted the decision for Atletico's penalty, but insisted the overturned call involving Eze was far harder to accept.
"We are all fuming about it," he said.
"When you have fought so hard for nine months to be in this position, that decision changes the course of the tie."
Atletico coach Diego Simeone saw things differently and praised VAR for correcting decisions during the match.
"The handball was not given at first, thanks to VAR it became a penalty," Simeone said.
"And the second penalty for Arsenal, thanks to VAR, was not a penalty. Sometimes VAR gives and sometimes it takes away."
The match itself was fiercely contested from start to finish at the Metropolitano Stadium. Atletico threatened early through Alvarez, while Arsenal captain Martin Odegaard and Noni Madueke both came close before the visitors broke through.
The home side pushed hard after equalising, with Antoine Griezmann striking the crossbar as Atletico searched for a winner. However, Arsenal held firm to extend their unbeaten run in this season's competition to 13 matches.
The result leaves the tie finely balanced ahead of next week's second leg at the Emirates Stadium in London.
"What do we have ahead of us? An extraordinary challenge," Simeone said.
"We will go there to play with everything we have."
Bukayo Saka has said Arsenal would head into next week's Champions League semi-final second leg with confidence after securing a hard-fought draw away to Atlético Madrid in Spain.
Manchester United midfielder Kobbie Mainoo has signed a new long-term contract with the club after an impressive return to form under manager Michael Carrick.
Milos Kerkez says he is "growing" into life at Liverpool F.C. as he continues to adapt to the demands and responsibility of playing for one of England's biggest clubs.
Tottenham winger Xavi Simons has already begun his road to recovery after suffering a serious knee injury that will keep him out for several months.
