Last season's runners-up drew 2-2 at 10-man Juventus to go through to the quarter-finals 3-2 on aggregate.
Drogba, who made it 2-2 on 83 minutes, also thought he had scored in the first half when keeper Gianluigi Buffon pushed his free kick against the post. Replays showed the ball had crossed the line but the officials did not have a clear view.
"Now technology is perfect so it must be done. So there is no dispute yes or no," Hiddink told a news conference as he revealed his PSV Eindhoven side in the 1980s had been involved in a goal-line technology trial.
"It was working out well but the people deciding didn't want to know. And that was 20 years ago."
Chelsea went behind twice to a Vincenzo Iaquinta strike and Alessandro Del Piero's contested penalty. Michael Essien brought them level at 1-1 just before the break before Drogba's close range finish after good work from Juliano Belletti.
"We knew if we were 1-0 or 2-0 down we should not panic as we knew we could score at any moment. What is good is that the team kept playing and reacted and we scored a beautiful goal through Belletti and Drogba," added Hiddink, who took over from Luiz Felipe Scolari last month.
Juve coach Claudio Ranieri, who also backed the use of technology, said his side had lost the tie in the first leg at Stamford Bridge when they lost 1-0.
"In this competition it is very important to score goals away from home. But I must thank the team for their great performance and the fans who really supported us until the last minute," the former Chelsea boss said.
"Conceding just before halftime was a like a cold shower after we had done well for 30 minutes."
