The Danes also benefitted from an Andreas Christensen goal, that cancelled out Shane Duffy's early header for Ireland, and a late Nicklas Bendtner penalty but Eriksen stole the show.
"I think we improved our game a lot and of course Ireland let us play a bit more, which we did".
Behind Christian Eriksen's brilliant hat-trick the Danes qualified for Russian Federation next summer, but Schmeichel felt a tinge of sadness that Ireland won't be able to join them.
He said: "We've lost the game, once we've lost the game, I'll have to go have a look at it". They were really poor goals to concede. "We were well beaten in the end".
"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. We are very much looking forward to it.
"We were chasing the game and needed goals to get back into the game but as we were trying to press, Denmark took advantage".
Set to a backdrop of clips from the qualification campaign just gone as well as some of the most famous moments in Irish football history, Gleeson can be seen urging the Irish players to "rage against the dying of the light", a line from the famous poem by Dylan Thomas, Do not go gentle into that good night.
Hareide is confident there is more to come from Eriksen, who is thriving in North London. "After scoring one goal it was a big knock for Ireland and it gave us the confidence to keep going".
Denmark booked their ticket to Russian Federation in style in the second leg in Dublin, running away with a tie that was in the balance after a goalless first game in Copenhagen. "That was the goal and aim before I started as the coach for Denmark and I am very pleased".
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.
"Denmark were stronger, they were better than us on the evening and well done to them".