Los Cafeteros closed in on the knockout stages after edging a fiercely contested Group C clash in Brasilia.
Monaco midfielder James Rodriguez fired Colombia ahead just after the hour with a powerful header from a corner, with substitute Juan Quintero adding a second on the break following a mistake by Ivory Coast midfielder Serey Die.
Drogba, the former Chelsea striker continuing to be troubled by a thigh problem, had not been called on until shortly before Colombia’s goal, replacing Swansea forward Wilfried Bony, with Salomon Kalou also having coming on for the closing stages.
A fine individual goal from former Arsenal forward Gervinho set up a tense finale, but the Elephants could not find an equaliser.
Ivory Coast had beaten Japan in their opening match, but may now well need victory over Greece to maintain hopes of making the last 16.
Lamouchi, though, insisted he always picked the side he felt were best equipped to get a result rather than worrying about individuals.
“I am not obsessed with Didier Drogba,” the Frenchman said after.
“If you look at the team, I have seen very interesting things from my players.
“It is just a few details that we missed, and that meant we lost the game.”
Lamouchi added: “My players did not deserve to lose, a draw would have been more deserved.
“It was a very experienced Colombian team who waited for us to make mistakes, unfortunately we made some and were hit in a hard way.
“We created some chances and came back to score, so I feel we lost unfairly.”
Lamouchi accepts the requirements for his side are clear heading into the showdown with Greece at Fortaleza on June 24.
He said: “We will need to go and fight to get a victory against Greece, it is very simple. I do not see any other way to qualify.”
Colombia have regrouped following the loss of star striker Radamel Falcao to injury ahead of the World Cup, and were cheered on by a reported 70,000-strong Tricolor contingent at Estadio Nacional Mane Garrincha.
Manager Jose Pekerman, however, insists there is still work to do for his side before they can think about making the knockout stages for the first time since 1990.
“It was a very hard match for us, and we must perform an analysis to see how the rest of the group will be set up,” said the Argentinian, who has gained cult status in Colombia after ending their 16-year wait for World Cup qualification.
Pekerman added: “It is, of course, a huge pleasure to see Colombia coming to this level, first of all at the World Cup after such a long period of time, and then having enjoyed two consecutive victories with players who are here for the first time, so they are all very positive situations for us.
“However, we cannot start thinking ahead of time or what might be coming later on.”
Ospina, Zuñiga, Armero (Arias 72), Sánchez, Zapata, Yepes, Cuadrado, Aguilar (Mejía 79), Gutiérrez, Rodríguez, Ibarbo (Quintero 53).
Barry, Aurier, Boka, Gonzaroua Die (Bolly 73), Zokora, Bamba, Gradel (Kalou 67), Tioté, Bony (Drogba 60), Y Touré, Gervinho