The midfield maestro, who had missed a couple of decent chances in the goalless playoff first leg, made no mistake in the Dublin return as his treble put the Irish to the sword.
Denmark goalkeeper Kasper Schmeichel has admitted he is "gutted" that Ireland won't be at the World Cup after the Danes knocked them out of contention for Russian Federation 2018.
"It's incredible to take your country to the World Cup with three goals in a playoff", said 25-year-old Eriksen. "We've been fighting for so long together after the two play-off games, which were very hard, but we got the result and we can be very pleased and I'm looking very much forward to World Cup".
However, Denmark bagged a third goal in the 63rd minute as Eriksen registered his second on the night with a fine effort from 20 yards.
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"I am really disappointed", said O'Neill.
"After scoring one goal it was a big knock for Ireland, we got a lot of confidence and started to play good football", said Eriksen, who plays for Premier League side Tottenham Hotspur. "They deserved to go through after beating us convincingly".
His first of the night came on 32 minutes, lashing a shot into the top left-hand corner of the net past Darren Randolph to make it 2-1. "That didn't happen and Denmark were clinical".
"Of course we got a lucky goal when Christiansen scored and after that it was just one-way".
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"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".
"That half was pure torture, I can not believe what I've witnessed tonight", Andrews told Sky Sports.
"He is one of the best players in the world but take that aside, as a guy and a person in the dressing room, he is a guy who can take the hopes of the nation on his shoulders and do magic with it. They are technically better than us and had a world-class player [Eriksen] in their team".
"Mentally I have grown up".
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