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A draw could also be enough, depending on the result in the other Group C clash between Colombia and Japan, with Lamouchi pleading for calm as Cote d'Ivoire go in search of setting a new national benchmark in the tournament.
"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,” the coach told Fifa’s official website.
“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.
Lamouchi then explained in depth the progress the side have made given their relative inexperience in the tournament.
"We mustn't forget that Cote d’Ivoire have only played eight World Cup games, which is nothing," he continued.
"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.
"We are trying to find our own style. We've been working together and building this group for two years now. We've got to know each other and want to stamp our mark on the pitch.
"I was happy with our performance [against Colombia]. I think there can be great victories in defeat and vice-versa.
"If we play like that, we shouldn't lose too many matches. And our opponents won't all necessarily have the quality that Colombia do."