Ireland knew a win against Denmark would secure an automatic spot in the tournament next summer but despite a positive performance and a late goal from Matt Doherty, Martin Braithwaite’s finish was enough to ensure the spoils were shared.
Following an uneventful opening to the game, the Danes suffered a couple of significant blows as both Thomas Delaney and Andreas Cornelius was forced to withdraw with injuries.
The Republic grew into the match and they finished the first half strongly but they just couldn’t edge in front before the break.
David McGoldrick caused the opposition’s defence numerous problems and after 34 minutes his over-hit pass sent Conor Hourihane through on goal but the Aston Villa man side-footed his effort straight at Kasper Schmeichel.
McGoldrick created an opportunity for Alan Browne moments later but the Cork native could only drive his half volley from distance narrowly wide of the far left post.
Mick McCarthy was forced to make a switch at the interval with John Egan being replaced by Ciaran Clark but the Boys in Green continued to play on the front foot.
Conor Hourihane again went close to breaking the deadlock at the beginning of the second half but following a clever short corner his cross was parried away by Schmeichel under severe pressure from the Irish attackers.
Ciaran Clark headed off target from a corner on the hour shortly before McGoldrick fired over on the turn as the home side pressed for the lead.
But as they began to pile players forward they left themselves open at the back and Denmark took advantage with 17 minutes remaining as they scored against the run of play.
Henrik Dalsgaard’s cross from the right-wing picked out the run of Martin Braithwaite and on the stretch, he managed to stab the ball past Randolph from close range.
The Irish battled until the end and they got an equaliser in the closing stages with Matt Doherty heading Enda Stevens’ cross home at the back post but it wasn’t to be as the visitors held on to the point that sees them finish second with Ireland third in Group D.
The draw for the play-offs will now take place on Friday.
REPUBLIC OF IRELAND: Darren Randolph; Matt Doherty, Shane Duffy, John Egan (Ciaran Clark ht), Enda Stevens; Conor Hourihane (Callum Robinson 68), Glenn Whelan (Sean Maguire 81); Alan Browne, Jeff Hendrick, James McClean; David McGoldrick.
DENMARK: Kasper Schmeichel, Simon Kjaer, Thomas Delaney (Pierre Emile Hojbjerg 13), Christian Eriksen, Martin Braithwaite, Mathias Jorgensen, Henrik Dalsgaard, Jens Stryger Larsen, Lasse Schone (Andreas Christensen 83), Yussuf Poulsen, Andreas Cornelius (Kasper Dolberg 33).
Referee: Felix Brych (Germany).