"Naturally, we're just pleased to be in the draw," O'Neill told reporters afterwards. "Being unseeded means it was always going to be a difficult tie. We're delighted to be in it.
"I know the Denmark manager, we used to play together. It will be an interesting confrontation.
"Now let's take our chance. I'm delighted to be drawn away from home first, so we'll try to get some sort of advantage, or negate their advantage, before we get to Dublin.
"That could have a big impact on proceedings, but we have to be going to Dublin with something still to play for. If you ask most coaches, you want the second game at home. But with the rules like extra time, it gives the away team that chance to score in 120 minutes.
"We have momentum and that's important. We won the last two games to get here. I'm now concerned with the next couple of weeks and making sure my players don't get injuries at club level."
Ireland have won four, lost four and drawn three of their 11 encounters with the Danes to date.