The Greeks conceded twice inside the opening six minutes against the Czech Republic in Tuesday's 2-1 defeat.
The same slow start afflicted them in their opening game draw with Poland where they went behind in the 17th minute.
Against the Poles, Greece fought their way back into the game but they left themselves too much to do against the lively Czechs and defender Jose Holebas said they can ill-afford another sleepy start.
"Every single one of us needs to have their mind on the game, and right from the start," he said.
"We must have the will to win the game and not only in the second half. We played better then and created some chances but this must happen from the first minute. You have to take control of the game to win it," he added.
Holebas said he could not understand why the team has been incapable of competing as well in the early stages of a game as in the latter.
"It's difficult to explain. It was like during the first game, the first 20-25 minutes... I don't know, we were asleep.
"We completely slept through the first 30 minutes, during the first half, it's as simple as that. For us it means a final against Russia, that's for sure. We need to get the three points, there's no other way," he said.
Greece had a goal harshly disallowed for offside before half-time but got back in the contest with a goal from substitute Fanis Gekas.
"We saw our mistakes and we tried to improve them, but again in the first minutes we performed really badly," said Gekas.
"The Czech Republic caught us napping, and managed to win the match. We tried to react to those two goals, but we couldn't.
"During the second half we started stronger - we wanted to react very quickly. We pushed ourselves to get the second goal but didn't manage it even though we had the chances," he said.
Saturday's clash with Russia in Warsaw will be a difficult test for Greece but they believe they have the resources to pull off a surprise.
"We still believe in our team and in ourselves, and we will keep going until the last minute of this tournament," said striker Giorgios Samaras.
