The two sides had drawn 0-0 in Copenhagen in the first leg of their play-off tie, and took an early lead in the second leg in Dublin.
But that was as good as it got as they ended up losing 5-1, with Tottenham midfielder Christian Eriksen scoring a hat-trick.
Newcastle's Ciaran Clark - who had captained his country in the first leg - started the match but was replaced by Shane Long in the 71st minute as Ireland chased the game. They were 3-1 down at the time.
Rob Elliot had left the squad to attend the funeral of his uncle, Ken.
Meanwhile, DeAndre Yedlin played the full game as the USA drew 1-1 with Portugal in a friendly.
Aleksandar Mitrovic was an unused substitute for Serbia in a 1-1 friendly draw against South Korea. He'd scored in last week's 2-0 win over China.