Argentina (18) 30
Winger Lucas Borges ran over to score Argentina's first try
Tries: Borges, Agulla
Pens: Contepomi (3)
Drop-goals: Hernandez (3)
Ireland (10) 15
Tries: O'Driscoll, Murphy
Ireland's disappointing World Cup ended with them failing to get out of the pool stages for the first time.
Eddie O'Sullivan's men needed to score four tries and beat Argentina by eight points to get through but they fell to a 15-point defeat at Parc des Princes.
Lucas Borges and Horacio Agulla scored tries for the Pumas in the first half.
Brian O'Driscoll got over for an Irish touchdown with Geordan Murphy briefly raising Irish hopes with a try early in the second half.
Argentina now play Scotland for a place in the semi-finals.
As for Ireland, the inquests will begin about where they went so badly wrong.
Disappointingly unconvincing wins over Namibia and Georgia and defeat by France left them with a mountain to climb against Argentina in the final Pool D match.
However, it started promisingly as Ireland had lots of ball in the opening 10 minutes.
But they failed to make their pressure count and it was Argentina who made the breakthrough.
Brian O'Driscoll scored a try for Ireland in the first half
After a solid scrum, the ball was worked to winger Borges who ran over with the Irish defence in a muddle.
Ronan O'Gara then kicked a penalty but Argentina replied instantly with a drop-goal from Juan Martin Hernandez.
Irish hopes were momentarily lifted eight minutes from the break when skipper O'Driscoll smashed through tame tackling for a try and O'Gara's conversion edged them into a two-point lead.
That advantage was shortlived as Hernandez produced a second drop-goal four minutes later.
Argentina punished slack Irish defending in the 38th minute with Agulla getting over for their second try and Felipe Contepomi converted, making it 18-10 to the Pumas at half-time.
It looked all over for Eddie O'Sullivan's men but hope flickered again when full-back Murphy scored a 47th-minute try after the ball was swung out to the right flank from a line-out.
That left Ireland 21-15 in arrears but knowing two converted tries would be enough to get them through to the quarter-finals.
However, two Contepomi penalties and a third Hernandez drop-goal sealed Argentina's victory to leave Ireland packing their bags for an early flight home.
Argentina: Corleto, Borges, M. Contepomi, F. Contepomi, Agulla, Martin Hernandez, Pichot, Roncero, Ledesma, Scelzo, C. Fernandez Lobbe, Albacete, Ostiglia, J. Fernandez Lobbe, Longo Elia.
Replacements: Basualdo, Hasan, Kairelis, Durand, Fernandez Miranda, Todeschini, Senillosa.
Ireland: Murphy, Horgan, O'Driscoll, D'Arcy, Hickie, O'Gara, Reddan, Horan, Flannery, Hayes, O'Callaghan, O'Connell, Easterby, D. Wallace, Leamy.
Replacements: R. Best, Young, O'Kelly, N. Best, Boss, P. Wallace, Duffy.
Referee: P Honiss (New Zealand)