Bayern Munich manager Carlo Ancelotti said referee Viktor Kassai "wasn't up to the task" of a Champions League quarter-final and called for video technology "as soon as possible".
Bayern midfielder Arturo Vidal was sent off for two bookable offences, while Real Madrid's Cristiano Ronaldo scored in extra time from an offside position as the Spanish holders won 6-3 on aggregate on Tuesday.
"We had thought of everything going into this game - except the referee," Ancelotti said.
"You can't decide a semi-final spot like this. It shouldn't happen at this level."
Ancelotti said Real manager Zinedine Zidane agreed with his assessment of Hungarian referee Kassai's "negative" performance at the Bernabeu.
"The referee probably wasn't up to the task," said the Italian, a former Real boss.
"I don't think Real Madrid have any influence on referees. The officials simply got it wrong. I had never been in favour of video technology, but I must admit it's necessary now."
Video assistant referees (VARs) are being trialled worldwide, with Fifa president Gianni Infantino keen to employ the system at the 2018 World Cup in Russia.
VARs - which rule on key incidents concerning goals, red cards, mistaken identities and penalties - could be used in English football as early as August, with the EFL Cup first round touted as a possible initial testing bed for the technology.
Video has already been used at international level, with two wrong decisions corrected by VARs as Spain beat France in a friendly in Paris on 29 March.
Uefa has not committed to the trials but in a statement said it was "constantly looking at ways in which it can improve the matches taking place in its competitions".
It added: "Regarding video assistant referees, there are currently trials taking place, so let's see the results and if or how the system can work while preserving the flow of the game."
'The referee killed it' - reaction
BBC 5 live pundit Pat Nevin: "I don't want the referee to have spoiled the entirety of this game because it was a fantastic tie over two legs - but the referee killed it with the sending off.
"It was terrible, and then he gets the decision wrong for Ronaldo's goal.
"The referee will probably get as much chat as anyone else."
Bayern chairman Karl-Heinz Rummenigge: "It was an extremely emotional spectacle, you can only compliment both teams. Our team has given everything, we must not forget that.
"It was great football, but unfortunately the referee gave some extreme decisions at our expense. The referee was of course the killer."