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The Ivorian striker believes the hard-earned victory will inspire the Blues to further success this season.
Drogba declared: "Arsenal are not there now, they lost the game, maybe it is going to be difficult for their confidence, I don't know, but I just try to look at my team and I think we did a good job.
"It is always difficult to play against Arsenal but we were compact and strong, we deserved it."
Bacary Sagna had put Arsenal in front but Chelsea stormed back with Drogba's double keeping them well in the hunt for the Premier League crown just five points behind Manchester United.
"It was an important win because it gives us the strength and the belief that we can still be champions," explained Drogba.
Joe Cole produced another outstanding performance against Arsenal and hinted that Arsene Wenger's side crumpled under their intense onslaught.
Cole said: "We both wanted to win the game so it was end to end, a draw wouldn't have been good for either of us, so we got the spoils.
"We were just a little bit more aggressive with our play.
"We got in their faces a little bit and when Didier plays as well as that you have got to use him, so we just kept knocking the ball up to his chest and joining him from there.
"We still think we can do it but we have to hope that Manchester United drop points and we win all of our games, but we will keep going, we are on a good run."