The team's plans for Thursday's (AEST) friendly and its Nations League opener against Wales on Monday were thrown into disarray by the situation, which it hopes is resolved before its next outing.
Spillerforeningen, the footballers' union of Denmark, made an offer to the Danish Football Association which would have seen established players feature in the two scheduled matches as normal under a temporary extension of their previous sponsorship deal, but the Danish authorities are said to have rejected it.
As a result, former international John Jensen was installed as temporary coach instead of Age Hareide and a 24-man squad made up of amateurs and semi-professionals travelled to Slovakia to avoid UEFA sanctions.
But they remained on level terms for just 11 minutes, before Adam Nemec headed Juraj Kucka's chipped right-wing cross in at the back post.
Jensen's men - none of whom had met their manager before travelling on Tuesday - initially responded well and went close twice in quick succession in the 25th minute, as Christian Offenberg narrowly missed Kasper Kempel's low cross, before Oskar Hojbye shot over from 12 yards.
Unsurprisingly, though, Slovakia remained in charge and eventually doubled its lead in the 37th minute - Albert Rusnak linking well with Kucka and finding the net from 14 yards.
Sadly for the Danes, the majority of the second period was played in their half and they were forced to cope with significant pressure.
And Slovakia eventually rounded things off 11 minutes from time, when Robert Mak's low cross took a deflection and then found the net via Denmark defender Adam Fogt.