Jurcic guided Dinamo to a record eight successive league title in April and his side topped the table after only six games of the new campaign but his third spell in charge ended abruptly after the surprise loss.
"We would like to thank Jurcic for everything he has done but we played only one decent game of football out of 12 in all competitions this season and we had no choice but to release him after a pitiful display against Austria," Mamic told the club's website after the loss.
"We have no options at the moment so Jurcic's assistant Damir Krznar will be in charge for the return leg against Austria on Tuesday where we hope to overturn the deficit," he added.
Dinamo missed a hatful of good chances before fine second half goals by Marin Leovac and Marko Stankovic put Austria in the driving seat to reach the money-spinning group stages of Europe's elite club competition.
Devoid of noteworthy attendances in the domestic league which lacks any real quality, playing in European competition and selling home-grown talent have been the two major sources of Dinamo's income and Mamic acknowledged elimination by Austria would be a bitter blow.
"A financial fortune is at stake here, apart from the club's reputation and fan joy, hence we will do everything we can to qualify and the least we can do is go down fighting if we are to be relegated into the Europa League," he said.
The losers of the Champions League play-off round will go into the Europa League group stage.