Finland gave themselves a chance of taking first place by beating Belarus 3-0 on Friday, keeping themselves three points behind Serbia, who recorded a 1-0 win at home to Hungary.
However, with the teams beginning the evening level on goal difference, a win of any kind for Finland would see them take top spot and automatic promotion.
Linda Sallstrom, fresh from scoring twice against the Belarusians on her 150th cap, came close to another goal in the 36th minute when her flicked header from a corner had to be clutched by Milica Kostic.
Group leaders Serbia had offered little going forward, and the only time they forced Anna Koivunen into a save before the break was when she comfortably caught Nina Matejic's effort from 20 yards soon after.
After half-time, the Boreal Owls were again threatening from corners, and Kostic again had to be alert to deny a goalbound effort, this time from Sanni Franssi.
The deserved breakthrough arrived 20 minutes from time - Katariina Kosola played the ball back to Evalina Summanen, who clipped in a cross which evaded everyone bar the late-arriving Nea Lehtola, who nodded in at the far post.
Finland were seven minutes plus stoppage time away from a place in League A, before disaster struck.
Substitute Milica Mijatovic went on a run down the left wing, and with no one in the box to aim for, was forced to cut inside. Her shot from a tight angle was easily saved by Koivunen, only for the ball to ricochet off the head of Maaria Roth and into the net.
Finland threw everyone, including Koivunen, up late on, but no winner meant Serbia preserved their three-point advantage to finish as group winners. Finland now await their opponents for the Promotion Playoffs, to be played in October.