Denmark booked their spot at the 2018 World Cup in Russian Federation after recording a 5-1 win over the Republic of Ireland in their second leg play-off tie.
The goal put him on a record 11 goals in World Cup qualifying for his country.
"We tried to play, and we got the openings, and we got the goals".
O'Neill had faced calls to be more expansive going into the game following a goalless draw in Copenhagen on Saturday, but quickly faced criticism after the defeat in Dublin for lacking caution, as Eriksen struck three goals and Nicklas Bendtner finished off the scoring from the spot late on.
Martin O'Neill bemoaned the Republic of Ireland's missed opportunities in the first half but admitted that Denmark deserved their victory as they won 5-1 in Dublin on Tuesday.
The former Republic of Ireland global was highly critical of manager Martin O'Neill who selected a diamond formation against Denmark, a change from his defensive five-man midfield which played in Copenhagen on Saturday.
"I'm naturally disappointed because a couple of nights ago in Copenhagen we had fought very, very strongly", O'Neill, who cut short an interview with national broadcaster RTE, told a news conference. Real Madrid and Barcelona can concede in the first minute and come back or they can score in the first minute and come back and lose the game.
"We're in this stage here and we thought we could win this game, but we didn't win the game, we were well beaten in the end and we have to take this punishment". We were more effective than in Parken, the effectiveness is very important in football.
Play switched rapidly from end to end with Duffy planting a firm header straight into Schmeichel's arms before Eriksen ran half the length of the pitch unopposed only to see his shot blocked by the diving Randolph.
"We have been fighting for so long to get to the World Cup".
"We'll take this with us and try to score as many goals as possible at the World Cup as well", said the midfielder, who doused former global defender Lars Jacobsen, who was broadcasting for Danish TV, with champagne as he celebrated.
"We've played 24 games in qualification over the last two campaigns and we've lost four games, tonight being the fourth time we've been beaten".