Chelsea had to wait until the 48th minute to break the deadlock through Anelka before Drogba struck from the penalty spot after the Ivorian was brought down.
Cole said: "At half- time the boss told us to keep going. At this period of time we have not been playing as well as at the beginning of the season. We had to pick it up.
"We need to improve as a team but with players like Nic and Didier - they stepped up to the plate and it was a great finish by Nico.
"Defenders drop off him and that gives us chances to score."