Lamouchi's men face their defining Group C fixture in Fortaleza on Tuesday, and are likely to require just a draw versus Greece to reach the last 16 for the first time.
The African side have been impressive thus far, coming from behind to beat Japan 2-1 in their opening match before falling to a tight defeat against Colombia.
Lamouchi has called for calm ahead of their final first-round clash, although he is aware of the game's significance.
He told FIFA.com: "We mustn't get carried away. We are fully focused on the match; we know that victory would allow us to write our names in Ivorian football history.
"That would be a great achievement and the players are well aware of that, so it would be pointless to try to heap extra pressure on them.
"We mustn't forget that Ivory Coast have only played eight World Cup games, which is nothing.
"There are no guarantees we will make it through: we have to come up with the goods on the pitch against a Greece team with a very solid backline. We are preparing with this in mind."
