Denmark and Switzerland secured spots at Euro 2020 at the expense of the Republic of Ireland on Monday as Roberto Mancini's Italy completed a perfect qualifying campaign by scoring nine.
Ireland needed to beat Denmark in Dublin to clinch qualification for next year's 24-team European Championship finals, but Matt Doherty's late header was only enough to earn Mick McCarthy's men a 1-1 draw at the Aviva Stadium.
A closely-fought contest, low on technical quality, swung the visitors' way when the unmarked Martin Braithwaite stuck out a boot to divert a Henrik Dalsgaard cross into the net on 73 minutes.
However, Ireland scored a late equaliser to draw 1-1 in Copenhagen in June and they repeated the feat here as Wolverhampton Wanderers right-back Doherty headed in an Enda Stevens cross with five minutes left.
Needing to win, the home side then threw everything at their opponents in the dying moments, but Denmark held on to clinch second place in Group D behind Switzerland.
"We had opportunities but I am not going to criticise the lads," McCarthy told Sky Sports.
"They have been brilliant. We lost one game out of eight. I am very proud of them. We can beat anyone in the play-offs."
"We need to improve various aspects of the game but for me it will be really difficult to leave some people at home when I select the squad for the finals. They would all deserve to be there."
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