Alex Telles won the tie after scoring a penalty with three minutes to play in extra time, following the use of VAR to determine Alessandro Florenzi had fouled Fernando in the area.
Roma then had a penalty claim of their own denied, despite a video referral, after Patrik Schick had claimed he was fouled in the box by Moussa Marega.
The Serie A side were involved in some controversy last season too when they claimed a string of decisions went against them in the second leg of their semi-final against Liverpool.
Speaking after the game on Wednesday, a frustrated Pallotta said: “Last year we asked for VAR in the Champions League because we got screwed in the semi-final and tonight, they’ve got VAR and we still get robbed.
"Patrik Schick was clearly clipped in the box, VAR shows it, and nothing is given. I’m tired of this crap. I give up.”
The Serie A side suffered a thrilling 7-6 defeat to Liverpool to miss out on a place in the Champions League final last season. Having lost the first leg 5-2, they won the second leg 4-1 in the Italian capital, but it was not enough.
Speaking that evening after watching his side narrowly knocked out by Jurgen Klopp's team, Pallotta said: "It is very clear VAR is needed in the Champions League because you just can't let stuff like this happen.
"You can all look at it yourself. Stephan El Shaarawy in the 49th minute wasn't offside and he gets taken down by the goalie; the 63rd minute was a handball that was obvious to everyone probably in the world except people on the pitch; the 67th minute Schick gets taken down in the box.
"I know it is difficult to ref but it is really embarrassing that we lose on aggregate like that.
"By the way, it should have been a red card which would have been 10 men in the 63rd minute.
"Liverpool are a great team, congratulations going forward, but if they don't get VAR in the Champions League stuff like this is an absolute joke."