A rampaging full-back at club level, Alaba is customarily deployed in midfield for his national team but Koller's tactical tinkering and fitness woes for first-choice striker Marc Janko contributed to him featuring in an unfamiliar No.10 role at the Parc des Princes.
Barring a storming run towards the end of the first period and a superb free-kick that was cleared off the line, Alaba struggled and made way for Alessandro Schopf.
Portugal's push for victory featured a missed penalty amid an intensely frustrating display from Cristiano Ronaldo but Alaba's plight meant the Real Madrid superstar was not the only stellar name to come up short in the French capital.
"We considered other options for the game and that was successful," said Koller after a point that keeps his team's qualification hopes alive - Austria's opening 2-0 loss to Hungary standing as the only Group F contest not to finish all square.
"David has played another position for us, more to the front. He did that quite well but I wanted to bring a little freshness to the side because the Portuguese were trying to win the game.
"Due to the intense defending, one or two players were quite exhausted at the end.
"It was difficult for Alaba, this new position. To play in this new position I think he did that very well together with [Martin] Harnik. Of course it was difficult for the two of them to play against such an opposition but they closed many spaces in the defence as well.
"I don't think there is any reason for him to be upset. He helped the side, he supported his team-mates. There is no reason to be upset or dissatisfied."
On a night where his side were under severe pressure for long periods, Koller understandably chose to praise goalkeeper Robert Almer.
"Robert Almer has always shown great games in the national side. Due to his size, being tall, he can anticipate very well and he has succeeded in that more than once," he said.
"He worked a lot. I'm happy for him. Before this tournament, he had an injury on the knee. But he was okay and he has all the qualities we need in a goalkeeper.
"He could have more self-confidence and he has shown a great effort. He contributed to the draw of our team."