The losing semi-finalists played-off in a third-place match and Argentina repeated the outcome of the opening game of the tournament, beating the host nation.
That opening match ended 17-12 in the Pumas' favour, but the result was even more overwhelming at the Parc des Princes on Friday, with Argentina recording a 34-10 victory and making a mockery of the pundits' claims that they had already gone one game too far in the tournament.
Leicester Tigers prop Marcos Ayerza was used as a 73rd-minute replacement and returns to Welford Road with his own bronze souvenir of his first World Cup tournament.
Loffreda's final game in charge of the Pumas could not have gone any better as his team ran in five tries through Felipe Contepomi (2), Omar Hasan, Federico Martin Aramburu and Ignacio Corleto.
Loffreda said: "This week was going to be really difficult for us but the players equipped themselves well. They played an incredible game, from a technical point of view every aspect was spot on.
"I am so proud, grateful, to all of them for the eight years we have spent together."