The Finns must now beat group leaders Hungary away on Sunday to stand any chance of finishing as one of the best third-placed teams and make it to January's tournament hosted by their neighbours Sweden, Norway and Denmark.
In front of a strong crowd at the Energia Areena in Vantaa, the home side took the lead in the opening minute through Santeri Vainionpaa, who then added his and Finland's second for a 2-1 advantage.
However, that was as good as things got for Finland, as Didier Dinart's men quickly stamped their authority on the match, opening up a three-goal lead for the first time when Radojica Cepic made it 7-4 in the 11th minute.
It was a gap that only extended, largely thanks to Finland losing their way in attack, failing to score for nearly seven minutes as Montenegro went from 14-10 in front to 17-10.
Miska Henriksson scored the final goal of the half to cut the lead to 19-12, but the Balkan side were still firmly in control.
Ola Lindgren's half-time team talk looked to have made little impact when Montenegro scored the first two goals of the second half, only for Finland to give themselves a sliver of hope with a 4-1 soon after to cut the gap to 17-23.
The Finns continued to have the better of the second half, and with nine minutes to go Linus Lindberg gave the home support reason to believe when he scored the third of a 3-0 run to make it 28-25.
But Montenegro made the ideal response, with three unanswered goals of their own to kill off the comeback, before closing out the 33-28 victory.
The result take the Montenegrins to seven points in the group, three clear of Finland with only two to play for. 2026 will be their eighth European Championship appearance as an independent nation.
Branko Vujovic netted seven times for the victors, outshone only by Vainionpaa, who scored eight.
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