The match officials allowed a crucial Filip Kostic strike to stand in the 36th minute despite the Eintracht Frankfurt wing-back clearly being in an offside position when he bundled home the rebound from Mijat Gacinovic's initial shot.
Frankfurt went on to win 2-0 in front of their own fans, levelling the tie at 4-4 on aggregate and advancing to the semi-finals via the away goals rule.
The incident magnified UEFA's move not to employ VAR until the May 29 final in Baku and Benfica boss Lage felt his touchline behaviour towards Italian referee Daniele Orsato did not warrant
"In the Europa League we have a small monitor near the bench and when I looked at it, I easily realised the player was offside," Lage told reporters after the match.
"I took two or three steps towards the fourth official and made the sign for VAR, which was maybe a fault of mine. We are so used to having the video referee.
"That's all it was. I was not offensive. We see so many coaches do more.
"The referee will realise he made a mistake, but we also have to look at our game.
"During the first half, the pressure was not as strong as we wanted. We got better in the second half, we tried to go looking for the result, and
"I believe that although we weren't as strong as in the first leg, we created enough opportunities to qualify."
Frankfurt sporting director Fredi Bobic admitted to taking a measure of enjoyment in the Benfica staff's apparent obliviousness to the absence of VAR.
"It's great that there are some mistakes [left in football]," Bobic said.
"I had to smile a bit because the whole Benfica bench asked for VAR. They should have known that in the Europa League you also have to be a little bit lucky. That's what we got."
Eintracht head coach Adi Hutter added: "You can give the first goal offside, but luck is sometimes needed. We defended well and maybe had the necessary fortune one or two other times."