The 39-year-old Argentine was forced off just 17 minutes into the game at the Renzo Barbera, sparking fears that the Nerazzurri legend's hopes of playing one more season at the highest level might have been dashed.
"The Zanetti injury was not what we wanted," Stramaccioni told Sky Sport Italia. "I'm not a medic but a lesion on the Achilles tendon does sound serious.
"To have lost Javier is a terrible blow in what was already a difficult period for us. It's difficult to comment on a situation like this."
Stramaccioni also found it tough to talk about his job prospects, with Inter now seventh in Serie A, two points outside the European places.
"This relates to our directors, the president," he stated. "I must think only of the pitch. And we will continue to give everything we have on the pitch.
"I should not be the one to talk about the future. We are thinking of playing right until the death."
Josip Ilcic scored the only goal of the game in Palermo, firing home just 10 minutes in after capitalizing on an error from former Rosanero defender Matias Silvestre, and Stramaccioni did not hide his disappointment at the manner of the winner.
"We conceded a goal from our own poor play and paid dearly for a mistake," the Roman lamented. "We then had chances to score, but we didn't have many options up front. The guys in the field, however, have given their all."
Inter now faces a daunting trip to the San Paolo to take on second-placed Napoli without the club's captain.