
The Danes had most possession and chances, with Christian Eriksen pulling the strings from midfield, but were unable to turn that into a goal in their third draw of the tournament.
They will await Uefa confirmation of whether they came second or third in the group – affecting who they face in the last 16 – depending on disciplinary points or rankings versus Slovenia who also drew 0-0 with England in their simultaneous game.
Serbia defended stoutly for long periods, but could not provide opportunities for veteran striker Aleksandar Mitrovic who appealed unsuccessfully for a penalty several times. They came fourth in the group with two points from two draws.
Both teams had goals disallowed, Denmark for a corner that went out of play and Serbia for offside.