The midfielder will miss Austria's friendly against the USA on Tuesday with an ankle injury, and Koller questioned why his club allowed him to report for international duty without being fully fit.
"We cannot tell Bremen what should be done, but it would be good if he could be built up correctly and get him to a stage where he is pain free and does not have to play with tablets or injections," he told the Bild.
However, Bremen coach Robin Dutt denied that Junuzovic had been unfit when he joined up with his national team.
"I have a good relationship with Marcel Koller and I don't think he means to blame us," Dutt said.
"If the player had been injured, he would not have left for international duty."
Junuzovic has earned 32 caps for Austria since making his debut against Canada in 2006.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.