Paul Osam's side conceded twice in the first-half, before Austria ensured the win with their third and final goal after the break.
Seven changes were made to the side that lost to Sweden on Friday night. Captain Seamas Keogh, James Furlong, Joe Hodge and Sean Kennedy all kept their places in the starting lineup.
Speaking after the game, Head Coach Osam said the side have some areas to work on ahead of their final game of the tournament on Tuesday.
"Our first objective will be to keep a clean sheet. We've tried to do that in the first two games. We hope to get a positive result."
Ireland's Under-16 side end their season with a game against Turkey, on Tuesday in Munkedal. Kick-off is at 11am (10am Irish time).
Republic of Ireland: Daniel Rose; James Furlong, Mazeed Ogungbo, Conrad Egan-Riley, Seamas Keogh; Joe Hodge, Matt Healy, Ronan McKinley; Ayodeji Sotana, Cillian Heaney, Sean Kennedy.
Substitutes used: Thomas Considine, Cian Kelly, Luke Turner, Conor Carty, Festy Ebosele, Leonardo Gaxha, Sean McGrath, Brandon Holt