Guus Hiddink's side drew 2-2 at Juventus on Tuesday to reach the quarter-finals 3-2 on aggregate.
Drogba netted his fourth goal in five games when he grabbed an 83rd-minute equaliser and was unlucky not to score in the first half when the officials missed his free kick creeping over the line.
Former coach Luiz Felipe Scolari was often reluctant to start the Ivory Coast striker but Hiddink, who took over from the Brazilian last month, has quickly restored the target man.
"He is very important," the Dutchman told reporters. "He doesn't give you an easy night as a defender.
"When he scores it is even better. He is doing very well. His goal, when he arrived just ahead of his marker, was a sign he is sharp."
Drogba's performance was all the more important given some of his colleagues struggled.
LACKED WIDTH
Goalkeeper Petr Cech was unusually shaky, John Terry was outpaced by Vincenzo Iaquinta for Juve's opening goal and the side generally lacked width.
Midfielder Michael Ballack also had another game to forget for the Londoners, beaten on penalties by Manchester United in last season's final in Moscow.
However, the return of goalscorer Michael Essien after six months out and Nicolas Anelka's display after a toe injury were positives for Hiddink, who does not care who Chelsea meet next.
"When you play in the last eight you play finals and can play English clubs as well. I don't have a preference," he said.
Juve coach Claudio Ranieri, whose side beat Real Madrid home and away in the group stages, was upbeat despite being eliminated by his former team.
The Turin club were in the competition for the first time since their Serie A demotion in 2006 for match-fixing.
"We have not done badly in the Champions League, we've played some great games. Considering where we were two years ago we've made huge leaps but can't be happy with that," said Ranieri.
Czech midfielder Pavel Nedved, injured early on Tuesday, is due to retire in May and Ranieri is eyeing reinforcements with Werder Bremen's Diego among those he is looking at.
"We are competitive but you need players year on year to make this leap of quality," he said.
