The 24-year-old has been tipped to be one of the standout performers in France but, while he impressed in the early stages, he failed to make a decisive contribution as Hungary took control of the Group F opener.
Koller said that playing Alaba in the middle, when he plays at left back with Bayern Munich, might explain why he struggled to make the right sort of impact.
"For us he plays in central midfield but for Bayern he plays in defence," Koller told reporters after his side were sunk by goals from Adam Szalai and Zoltan Stieber. "Maybe that creates a bit of a problem."
Alaba, who often captains the team, sent a rasping shot against keeper Gabor Kiraly's post in the opening minutes.
However, he was generally outshone by 37-year-old HungarianZoltan Gera.
"If he had scored a goal with his early chance you wouldn't be questioning him," Koller added. "We saw today that Alaba has an excellent technical side to his game."
While the skipper delivered a number of fine passes, and dribbled well, he was wasteful in front of goal, taking six shots and only testing Kiraly once.
Austria's next game is against group favourites Portugal in Paris on Saturday.
(Editing by Tony Jimenez)
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