Chelsea’s Thierno Ballo gave Austria the lead before Junior Chikwubuike Adamu made it two on 77 minutes.
Ireland ended the match with nine men after Barry Coffey and Adam O’Reilly were shown straight reds by referee Kirill Levnikov.
Ireland went into the game knowing a 1-0 win could have been enough for qualification. The first half was an even affair with both sides tussling for possession. Ireland were composed on the ball and looked to use the pace of their forward line to cause the hosts problems.
But it was Austria who took the lead on 26 minutes. Ballo saw his effort blocked by the Irish defence. To his fortune the ball found its way back to the midfielder who made no mistake in finding the net with his second attempt.
From that point Ireland took control of the game with Noss and Coffey orchestrating the play from the midfield.
Austria had a glorious chance to make it two when a speculative effort was drove towards goal. Marlon Mustapha, who appeared to be offside, managed to steer it first time to Ivan Šarčević who somehow scooped his shot over the bar.
Then on 42 minutes it got worse for Ireland when Coffey was shown a straight red card for a challenge on Adamu. From the resulting free-kick Mustapha headed onto the bar before the danger was cleared.
After the break it was Ireland who started the stronger of the two sides. With Switzerland beating Gibraltar in the other group game Mohan’s team had to score at least three to progress. Wright had an effort on the hour mark but he couldn’t find the finish and his attempt went harmlessly wide.
On 65 minutes they found themselves down to nine men when O’Reilly was shown a red when he was on the end of rugby type tackle on the halfway line and retaliated. It presented Ireland with a huge task and they looked to get back in the game as they sought to attack at every opportunity.
However, Austria doubled their lead when Adamu found space in the 18-yard box to place it past Jimmy Corcoran.
They were given a glimmer of hope when Switzerland were reduced to 10 men after Patrick Wimmer received a second yellow but it wasn’t to be for Ireland who finished third in Group 10 and miss out on the next stage of qualifiers.
Speaking about the loss Republic of Ireland Under-19 Head Coach Tom Mohan said: "Ill discipline has cost us today. Perhaps, with so much riding on the games, players are losing their heads in the heat of the battle. At this level you have to keep your composure and that wasn't the case.
"Austria are a very good team and I felt we contained them for large parts of the game. The first goal came as a sucker-punch and even with 10 men, we still tried to play and create. My team gave me everything - they never stopped - but it wasn't to be our day."
Mohan also looked back on the tournament and the progress the Under-19 side has made throughout 2019. He added: "The result is still raw and it has been a rollercoaster year but let's not lose sight of the bigger picture and what has been accomplished.
"We have six players eligible for the Under-19s in the Under-21s side as well as Troy Parrott at senior level. This is excellent to see and shows you the strides being made at underage level in Ireland."
Ireland: Corcoran (GK), McGuinness, McEntee (Richards 90) Omobamidele, Ogungbo; Coffey, O’Reilly, Noss (Sobowale 82); Ebosele (Gilbert 90),Wright (Tierney 81), Cassidy (Oko-Flex 70).
Austria: Maric (GK), Schofl, Aigner, Affengruber, Wimmer; Šarčević (Daniliuc 46), Velimirovic (Hahn 67) Prass, Mustapha (Steiger 46), Adamu (Abdijanovic
90) Ballo (Berger 26)
Referee: Kirill Levnikov (Russia)