"It's an incredible feeling", he told Sky Sports.
The Republic of Ireland endured a nightmare night in Dublin on Tuesday, with the hosts taken apart by a magnifcent display from Christian Eriksen.
"I was surprised really because they played in a diamond - the midfield - with two forwards, and our centre-halves can handle two forwards, but that gave a lot of space in centre midfield for Eriksen.""We were well beaten in the end".
"I don't agree with our luck running out, it was a commendable effort by the team".
"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".
Former Leicester and Celtic manager O'Neill's defensive style of play has often been criticised and his side scored three or more goals in a single game just once in their 12 qualifying and play-off matches.
Eriksen, who has scored 21 times in 75 internationals, said there were more goals to come from Denmark in Russian Federation.
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.
Eriksen bagged his second of the game on 63 minutes, again producing a superb finish after good work from the effervescent Pione Sisto. "That was the goal and aim before I started as the coach for Denmark and I am very pleased".
The Irish were much improved from their toothless first-leg display and had a couple of chances to increase their lead, with Daryl Murphy and James McClean both going close.
"I'm very pleased for the team, this is a hard place to play football - they're compact and good defensively, so scoring five against Ireland does not happen very often. We've been fighting for so long to get there (to the World Cup) and of course now the two play-off games were very hard but with the result we got tonight we can be very pleased and it makes you very much looking forward to the World Cup".