PSG looked to be in cruise control at the Santiago Bernabeu after Kylian Mbappe gave them a first half lead, extending their 1-0 advantage from the first leg.
However, once Karim Benzema dispossessed Gianluigi Donnarumma in the 61st minute leading to the hosts equalizer, PSG crumbled.
Benzema completed a 17-minute hattrick to help Real Madrid win 3-1 on the night and advance 3-2 on aggregate.
Pochettino believes VAR should have disallowed Real Madrid’s first goal as he fouled Donnarumma in the build-up.
"What a shame, there is a foul on Donnarumma for the first goal," Pochettino told Canal+.
"It is not possible to not talk about this gross mistake. It is not possible for this to happen in 2022.
"Real Madrid's first goal changed the game. I wonder what the VAR does because there is a foul. It's a shame. When you see the action, it's a foul.
"After that, the match changed. For 60 minutes we dominated and that goal changed everything.
"It's not easy to explain the defeat. After the goal, the nervousness and the feeling of injustice hurt us a lot. The little details mark these games. We felt the impact of the equalising goal."
"The rest of the season is going to be very difficult," he added. "The Champions League has been PSG's goal for years, everyone knows it. The fans are going to be upset, we know it.
"At a time like this, we will still have to analyse and remember the good things we have achieved against this excellent Madrid team. But what happened tonight is not normal."
