Drogba injured his thigh in training on Thursday and started on the bench in Ivory Coast's FIFA World Cup opener on Saturday, with Lamouchi selecting Wilfried Bony up front in Recife.
Without Drogba, who had scored seven goals in his past nine appearances for his country, Lamouchi's side appeared to lack ideas in attack as they chased Japan, who took the lead in the 16th minute at the Itaipava Arena Pernambuco through Keisuke Honda.
Lamouchi brought Drogba on in the 62nd minute and although the 36-year-old did not create or score either of Ivory Coast's goals, the French coach claimed the bustling striker made a big difference.
"We didn't start the game very well by conceding through a lapse in concentration," Lamouchi said.
"After that, we got into a lot of good positions. For us it was really important to start well this tournament. To have a player like Didier Drogba in your squad, as a starter or a sub, changes a game."
Within a minute of coming off the bench, Drogba almost set up a goal with a clever back-heel in the area, which Gervinho could not capitalise on.
Soon after, Bony equalised with a header from Serge Aurier and when the right-back crossed for Gervinho two minutes later, Ivory Coast were in front.
Drogba could have stretched his team's lead even further late in the match as his powerful free-kick was parried away by Eiji Kawashima and a shot from the edge of the box was deflected just the wrong side of the post.
But despite that, Ivory Coast held on to win their opening game at a World Cup for the first time.
At the previous two World Cups finals, the Ivory Coast failed to get out of their group after missing out on victory in their first match, although Lamouchi underlined that winning the opening game was not a guarantee of reaching the round of 16.
"The players are very happy with the victory but we are not yet qualified," he said.
Ivory Coast face Group C leaders Colombia on Thursday in Brasilia.
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