George Burley's side needed three points against the runaway Group 9 leaders at Hampden last night to have any chance of a play-off spot.
However, an 81st minute goal by Holland substitute Eljero Elia dropped Scotland into third place in the section behind Norway and sent the Tartan Army home wondering what might have been if Kenny Miller had not missed a second-half chance when the game was goalless.
Former Rangers defender Van Bronckhorst, who played for the Ibrox club between 1998 and 2001, was pleased that the Dutch made history of their own by completing a clean sweep of qualifying wins, but took no pleasure from dumping out the Scots.
"I had mixed feelings going on to the pitch because you want to win for your country, but you know if you win then Scotland will be out.
"If Kenny had another chance like that, then he would score," Van Bronckhorst said.
"It was a big chance, but our keeper did tremendously well to save and it was a big turning point in the game.
"But we got eight wins in a row and finished with 24 points which is a great compliment," he said. "We will possibly be in the first pot of seeds for the World Cup so that is important for us."