Chelsea's 4-1 victory over Spartak Moscow ensured that they qualified for the knockout stages of the competition, with two goals from Branislav Ivanovic and another from Nicolas Anelka complementing Drogba's penalty.
But now Chelsea face a difficult away trip to Liverpool on Sunday and Drogba, who captained the side against Spartak in the absence of the rested John Terry and the injured Frank Lampard, wants the Blues to maintain their healthy five-point lead at the top of the Premier League.
Liverpool's poor start to the season under new boss Roy Hodgson has been softened in recent weeks by successive victories against Blackburn and Bolton.
And Drogba believes that Liverpool, who will be without former Chelsea star Joe Cole through injury, will look to keep their revival going against Carlo Ancelotti's side.
"There is never a good time to go to Anfield because they are a very strong team," said Drogba. "They will try to use this game to start their season, so we have to be ready.
"We are seeing a different Liverpool than the one from earlier in the season. They have won their last two matches and their confidence is getting higher.
"We have to be careful. It's true that we shouldn't fear any team but we're going to have some difficult moments. Since I've been here, Chelsea v Liverpool has been special and it's always a difficult game. We're going there to win but it's not going to be easy.
"The most difficult opponent is ourselves. We know if we lose points like we did last year we can be in trouble again. It's down to us to keep winning and to keep the gap.
"It's not easy. There are only a few teams who have done it before. When we lost against Manchester City, the reaction was good and that's what we have to try to achieve."
But Drogba is certainly not getting carried away by Chelsea's position at the summit of both the English top flight and Group F of the Champions League.
He missed the opening two games of the European campaign through suspension and then a virus prevented him from playing in the first match against Spartak in Moscow.
A point against MSK Zilina at Stamford Bridge in a fortnight will ensure the Blues finish top of the group, but Drogba remains cautious over Chelsea's chances of winning the trophy at Wembley in May.
"Last year we were in the same position," added Drogba. "We qualified with two games to go and then we were out in the last 16.
"I can't say I'm happy to have missed the first few games because I'd have preferred to help my team achieve victories.
"But I hope the break is going to help me in future games. It's not easy because as a player you want to keep playing so you can find your best physical condition and understanding with your team-mates.
"I missed that a little bit before and that's why sometimes it was difficult for me at the start of league games but hopefully now I am going to be able to play regularly."