Yet Orsic’s two second-half strikes took the match to extra time and the 28-year-old winger scored a superb third on 106 minutes to clinch the match ball and a famous victory.
Spurs pushed for a late away goal that would have been decisive but substitute Gareth Bale and Kane were both denied by two excellent Dominik Livakovic stops in the Dinamo goal.
And the north Londoners ultimately failed to find the back of the net in the closing stages and crashed out to leave their hopes of playing Champions League football next season hanging by a thin thread.
Spurs sit eighth in the Premier League and while they have a game in hand that could move them three points behind Chelsea in fourth with a win, the Blues are in formidable form having gone 13 unbeaten across all competitions under Thomas Tuchel.
And Mourinho told BT Sport in Zagreb: “If I forget the last 10 minutes of the extra time, where we did something to get the different result and go through, in the 90 minutes and in the first half of extra time, it was one team that decided to leave everything on the pitch.
“They left everything there, sweat, energy, blood. In the end they let even tears of happiness out. Very humble. Very committed. I have to praise them.
“On the other side my team, I am there, didn’t look like they were playing an important match. If for any one of them, it is not an important match… for me it is, for the respect I have for my own career and job. Every match is an important match for me.
“For every Tottenham fan at home, every match matters. Another attitude is needed. To say that I feel sad is not enough. What I feel goes much further than sadness.
“Football is not just about players who have more quality than others. The basics of football go beyond that. It’s the attitude and they beat us on that.
“Many teams I fear my thoughts, my feelings. But I don’t blame myself in the sense that I always share them. Before the game I told the players the risk of a bad attitude and even at half-time at 0-0, the risk of playing the way we were playing.
“It happened. I believe the players only realised that the game was at risk when they scored the second goal and it went to extra time.”
Spurs’ European misery follows their north London derby defeat to Arsenal at the Emirates last Sunday to complete a grim week for the club.
“I repeat, because I don’t want any doubts about it, I feel sorry that my team – I belong to that team – I feel that my team didn’t bring to the game, I feel, not just the basics of football but the basics of life, which is to respect our jobs and give everything.
“I feel deeply hurt with what happened with my team. On behalf of my team, in spite of maybe some of them, they don’t share my feelings and my emotions, I can only apologise to the Tottenham supporters.
“I hope that the players feel the same way that I feel. Today is, of course, live or die and in this moment we died.
“In the Europa League it’s not the first time. In Antwerp I had, of course not a feeling of the same dimension as it was a group phase and we had a chance to win it and to go through.
“But it’s a feeling I have, and some other matches I had the same feeling, but until the last day of the season we have to try to do our best.”