Silkeborg had already given themselves poor odds for going through to the playoff round in the qualifying phase of the tournament when they suffered a 1-0 defeat at home a week ago.
The Danes were immediately put under pressure at the intimidating Bialystok City Stadium, and after hitting the woodwork twice in quick succession, the home side took the lead after 27 minutes, when Jesus Imaz got on the end of a curling cross from Alejandro Pozo.
That inspired the hosts to intensify the pressure on the Danish goal, and the Silkeborg rearguard was forced to surrender again just five minutes later when Imaz was on target again to double the Polish lead.
Jagiellonia had chances to make things even worse for the visitors in the second half but against the run of play, Silkeborg reduced the deficit shortly before the end of the match when Sofus Berger scored from the edge of the box.
It was, however, too little too late for the Danes against a superior Polish side.