"You could see that it was very influential when he was on the pitch," LaMouchi said, highlighting the attention Drogba drew from Japanese defenders. "He created space for the players."
A mere two minutes after the talismanic striker's arrival, Wilfried Bony and Gervinho scored with headers two minutes apart. Both goals were set up by curling crosses from defender Serge Aurier.
"It's true that after (Drogba) came in, they had more confidence," said Japan goalkeeper Eiji Kawashima. "It changed the match."
Lamouchi's inspired substitution negated Keisuke Honda's first half goal that had given Japan the lead in a group that also includes Colombia and Greece. Colombia beat Greece 3-0 earlier on Saturday.
"I didn't think we were able to play as quickly as we normally play and needed to do," Japan coach Alberto Zaccheroni said. "We really have to take stock of the situation rather quickly."
The 36-year-old former Chelsea star started for Ivory Coast in the last two World Cups, but neither of those sides made it out of group play. He probably lacks the fitness to play 90 minutes these days, but his impact as a substitute can be dramatic, as was shown on a rainy night in Recife.
Lamouchi said it wasn't easy for him to leave Drogba on the bench from the start, but credited Drogba for the way he handled the decision.
"To see the joy he experienced at the end of the match ... I am convinced he's a champion and we need him," Lamouchi said.
Now the Ivory Coast is in good shape to advance to the second round for the first time. Next up is Colombia, the group leader by virtue of goal difference. That match is Thursday, as is Japan's next test against Greece.
"We have to keep morale high because we know we can play better," Zaccheroni said.
Japan had the better of the play in the first half, taking the lead through Honda's hard left-footed strike from about 12 yards in the 16th minute.
Yuto Nagatomo slid a pass across the edge of the penalty area to Honda, who settled the ball cleanly with his right foot before belting his 21st career international goal under the cross bar and inside the near post.
Japan had several chances to widen its lead in the opening 45 minutes, and will rue missing them.
Just minutes after Honda's goal, Japan defender Atsuto Uchida made a run down the right and unloaded a point-blank shot that Ivory Coast goalkeeper Boubacar Barry parried. Honda's curling shot from the edge of the penalty area soon after forced Barry to make a leaping save.
Ivory Coast dominated the second half but the sluggish-looking team was making little headway until the arrival of Drogba galvanized it. Within minutes, Bony's angled header found the goal and then Gervinho scored with a near post header that Kawashima should have saved.
Japan could not make any impression on the Ivory Coast defense in the remaining 20 minutes.
The game marked the World Cup debut for Lamouchi, a 42-year-old Frenchman of Moroccan descent who was widely seen as a surprise hire in 2012. It was also an unpopular move among fans in the Ivory Coast, who favored a more experienced coach for a team which has been to the previous two World Cups, and which has a number of players who have flourished in Europe's top professional leagues.