Touted as dark horses before the tournament, Austria have struggled to reproduce their impressive qualifying form and are bottom of Group F with just one point.
But after a 2-0 defeat to Hungary and goalless stalement against Portugal, a victory over European Championship newcomers Iceland could still send Austria through to the last 16.
Iceland also have ambitions of reaching the knockout phase and Koller, who faces mounting pressure despite signing a two-year extension in March, knows Austria face a real scrap to avoid elimination.
“We certainly can’t presume that the game against Iceland will be easier,” he said. “It will be a very uncomfortable game.
“They’re very disciplined, strong in the tackle and compact defensively as they’ve proved in their two games here.”
Koller said Zlatko Junuzovic was recovering well from an ankle injury sustained in the opening game, and although the Werder Bremen midfielder’s status remains unclear, centre-back Aleksandar Dragovic is available again after serving a one-match ban.
“I don’t need to do much to build the players up,” added Koller. “The mentality will be there. We’re still in the race after (the Portugal draw) and we’ll have a ‘final’ on Wednesday.”
David Alaba fired against the post inside the opening minute against Hungary in Austria’s first game, but the Bayern Munich star has struggled to impose himself since and was replaced after 65 minutes against Portugal.
“I don’t think there’s any reason for him to be upset. He did what he had to do when he was on the pitch,” Koller said after the Portugal match, springing to Alaba’s defence.
“He has no reason to be upset or unsatisfied. We have a third game ahead and that will be very important in order to advance.”
Iceland, with a population of just 330,000, are the smallest nation ever to compete at the finals of major tournament and have acquitted themselves well in France.
The Nordic islanders celebrated a hard-fought point in a 1-1 draw with Portugal, but Iceland suffered contrasting emotions when a late own-goal handed Hungary an equaliser in another 1-1 draw on Saturday.
“It feels like a loss. The dressing room was silent after the game, we were so close to securing (qualification),” said Kolbeinn Sigthorsson.
But Helmir Hallgrimsson, who shares head coaching duties with Lars Lagerback, said Iceland were pleased to still be in control of their destiny.
“Everything is in our hands and we are happy at the moment. If someone had given us this before the finals we would gladly have taken it. We go into the game to win it,” he said, although Iceland have never beaten Austria.