The Danes booked their ticket to Russian Federation with a brilliant 5-1 win in Dublin, Eriksen's treble sandwiched by a Cyrus Christie own goal and Nicklas Bendtner penalty after Shane Duffy had put the hosts into an early lead.
Asked if Eriksen could be considered as one of the top 10 players in the world, Hareide said: "Yes, absolutely in the top 10".
Denmark has qualified for the 2018 World Cup, and Christian Eriksen played the role of the hero.
"We're really disappointed", O'Neill said following the heavy defeat. They play football - we saw against Real Madrid that it suits him very well to play there.
Not surprisingly, McClean, one of Ireland's better performers on the night, was distraught at the end of the game.
"That is simply not true", he insisted, adding that he hadn't won the "trophies that I have won both as a player and manager" because of luck.
"The disappointment is obviously very, very strong tonight because we haven't been able to do it, but I have to commend the players on getting this far".
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They also have an inscription in raised dots that helps blind and partially-sighted users to identify them. The foil image over the see-through window is Winchester Cathedral, where Austen was buried in 1817.
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They were hammered 5-1 by Denmark in tonight's play-off at the Aviva Stadium in Dublin, having drawn the first leg 0-0.
But Denmark stormed back and tore Ireland apart.
If Denmark's first goal, an own goal by Cyrus Christie, was a bit disheartening for the Irish, Eriksen's wonder goal in the 32nd minute completely broke them.
The Canaries legend was an unused substitute on Saturday night as Martin O'Neill's team held the Danes to a 0-0 draw in Copenhagen in the first leg. It's a big thing and I'm very, very happy about it.
If we did need firing up for the game, however, then RTÉ Sport, as they often do in these situations, have provided the flawless tonic with an inspirational promo starring none other than Brendan Gleeson for the big game.
Eriksen bagged his second of the game on 63 minutes, again producing a superb finish after good work from the effervescent Pione Sisto.