Atletico defender Marc Pubill touched a ball passed to him by goalkeeper Juan Musso with his hand, to set it still in order to take the goal-kick himself, which Flick said should have been a red card and a penalty.
In the first half VAR intervened to get referee Istvan Kovacs to review an incident involving Barca defender Pau Cubarsi, who was booked for felling Giuliano Simeone as he ran through on goal.
After the review Barca defender Cubarsi was sent off, leaving the Catalans with 10 men for the second half.
"The VAR was very focused today for Atletico, he's a German guy, so thanks Germany," former German national team coach Flick told reporters. "It's for me a clear red card."
In 2024 Aston Villa's Tyrone Mings was punished for a similar infringement in a Champions League defeat against Club Brugge.
Flick said the VAR officials should have asked Kovacs to review the incident.
"For my perspective it's clear, he has to call and say okay come on look at this, the same like before. I don't understand," added Flick.
"I haven't spoken with the referee. I think it was better not to speak with him.
"We have to accept it, and focus in the match next Tuesday in Atletico. We have the quality, the players who can decide (this game) and we have to fight."
Barcelona defender Ronald Araujo said it was "absurd but a clear penalty".
Atletico coach Diego Simeone said the officials were correct not to intervene.
"There's common sense," said the Argentine.
"If Marc, who was supposedly receiving a pass to start the play, interpreted it the way he did, and the referee interpreted it the same way Marc did, it's because there is only common sense about the play."