Atletico won 2-0 in the first-leg of their quarterfinal thanks to goals from Julian Alvarez and Alexander Sorloth. Pau Cubarsi was sent off - via VAR - for Barca before Alvarez's opener.
Flick said: "We lost, but we had some very good opportunities. We're not going to give up. I think we had a lot of chances.
"I don't know about Cubarsí's sending off; it could have been a red card, or it might not have been. I'm not sure if he touched him enough. The ball was behind him."
The German then went on to slam the decision for VAR to ignore Atletico fullback Marc Pubill handling the ball inside the area. The defender grabbed the ball after a goal-kick had been taken, believing the referee was calling for a restart. Both the match officials and VAR appeared to excuse Pubill's actions and the goal-kick was retaken.
Flick continued: "The situation where they handled the ball in the area... I don't understand why VAR didn't intervene. It's normal to make mistakes, but in these kinds of situations, what's the point of VAR? It should be a penalty and a second yellow, a red card.
"They scored two goals and showed great quality. We need to defend better for the first goal; we got a red card and then they scored.
"VAR was pretty biased in Atlético's favor... it was a German official? Thanks, Germany. I don't know what happens when a goalkeeper starts to play the ball and the defender stops it with his hand; for me, it's a second yellow card and a penalty.
" I hope they can explain it to us. I think we gave it our all and weren't lucky, but we have to focus on the next match against Atlético. We're positive, we'll fight."