Cubarsi, 19, was shown a straight red card for a last man tackle on Atletico’s Giuliano Simeone just before half time at the Camp Nou.
Referee Istvan Kovacs initially showed a yellow, but VAR intervened and it was changed to a red. Atletico striker Julian Alvarez then gave his side a 1-0 lead from the resulting freekick.
Speaking to reporters after the game, Flick was furious with the decision but insisted his side can still turn it around in the quarter-final’s second leg.
"We lost 2-0 but we have a good chance in Madrid. We don't give up, we have a chance still,” he said.
"I don't know (about the red card), I'm not sure how much he (Cubarsi) touched him. The ball was behind him.
"When they (Atleti) player touched the ball (at a goal-kick) it's clear, why not VAR? It's unbelievable.
"We all make mistakes, it's normal, but this situation. Why do we have VAR? I cannot understand. Normally it would be penalty and a red card. Double yellow is a red.
"Of course we believe (we can do it), second half we played well with one player less."