After their opening-round victory over Greece, the South Americans sit top of Group C, ahead of their next opponents on goal difference.
Zapata insists Colombia know what to expect from Ivory Coast in Brasilia.
Gervinho netted the winning goal as the African nation triumphed against Japan on Saturday, but the Roma forward's pace is an asset Zapata is well aware of having faced him at club level with Milan.
"Sure, I have faced (him before)," he is quoted as saying in El Espectador. "(He is) fast and skilled.
"We have to stay focused, we are also fast and have our (own) qualities."
The introduction of Drogba proved key to Ivory Coast turning around their match with Japan.
Wilfried Bony and Gervinho each found the net within five minutes of the veteran striker's introduction.
"Drogba's a beast inside the area," added Zapata. "You have to stay focused throughout the match and mark very closely.
"We are a humble squad that knows how to win and does not suffer from overconfidence, we go step-by-step.
"We are mentally prepared to take the fight."
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