With the score tied in the final stages Eberechi Eze went down in the box under a challenge from Atletico defender David Hancko, who made contact with his foot.
Dutch referee Danny Makkelie pointed to the penalty spot but changed his mind after a VAR review to the delight of the Metropolitano stadium.
"What I'm incredibly fuming with is how the hell the penalty on (Eze) gets overturned in the manner that it happened," Arteta told reporters.
"This changes the course of the game at this level. I'm sorry but this cannot happen."
Arsenal took the lead after Hancko fouled Viktor Gyokeres, who scored the resulting penalty, before Julian Alvarez levelled with another spot kick early in the second half after a Ben White handball.
Arteta said he could accept that decision, after a similar penalty was given against Bayern Munich on Tuesday in the other semi-final, but he could not stomach the reversal of the Eze call.
"We are all fuming about it," continued Arteta.
"When you have fought so hard for nine months to be in this position, that's another goal that changed completely the course of the tie.
"This cannot happen. We put so much (into) it, it cannot happen."
By contrast his opposite number Diego Simeone was grateful for VAR's interventions, after the White handball was also only given following a review.
The Atletico coach also disagreed with the decision to award Arsenal a spot kick for Hancko's challenge on Gyokeres, shoving the striker's back.
"The first penalty, in my humble opinion, there is some contact behind and the player throws himself down, in the semi-final of the Champions League, I think a penalty really needs to be a penalty," said Simeone.
"The handball was not given as handball, thanks to VAR it was a penalty, and the second penalty thanks to VAR was not a penalty. Sometimes VAR gives and sometimes it takes away."
The draw leaves everything to play for in the second leg in London on Tuesday, with both sides desperate to win the trophy for the first time.
"What do we have ahead of us? An extraordinary challenge," said Simeone.
"London, Arsenal's ground, a team that has not lost at all in the Champions League.
"We have huge hope and we will go there to play with everything we have."