The earlier match is subject to a FIFA investigation following irregular betting patterns but what will worry Batista more is that he has yet to come up with a formula less than a month out from the start of the Copa America, which this summer is on home soil.
Adrian Mierzejewski and Pawel Brozek got the goals for Euro 2012 co-hosts Poland, sandwiching an effort from Marco Ruben just after the interval.
At least Ruben's goal on his debut was a bright point for the albiceleste, who are reshuffling their pack after the departure of Diego Maradona following a World Cup which started well but ended in a quarter-final thumping by Germany.
After the nightmare in Nigeria, Batista made seven changes and elected an all new strikeforce in the shape of Ruben, Jonathan Cristaldo and Pablo Piatti.
But even if Batista can point to the fact that only two Copa America starters - Pablo Zabaleta and Ezequiel Garay - featured in what was essentially a B team, another defeat will not have done much for morale.
Robert Lewandowski set up the opener for the Poles on 26 minutes, Mierzejewski finishing neatly as central defender Federico Fazio was caught out and although Piatti set up Villarreal's Ruben with a backheel for the equaliser - the latter had already gone close minutes earlier.
Mierzejewski, freshly elected player of the year in Poland, went close again just after the hour but keeper Adrian Gabbarini made a fine stop.
However, in the 67th minute Poland sealed the win as Brozek, a second half substitute, took a pass from Jakub Blaszczykowski and finished with aplomb.
Argentina, whose last South American title came in 1993, will at the Copa face Bolivia, Colombia and Costa Rica, who are standing in for a Japan side which withdrew owing to the effects of the tsunami earlier this year which forced a backlog of domestic J-League fixtures.
Since their last triumph in the continental showpiece Argentina have seen rivals Brazil win the event four times - losing the last two finals to the auriverde.