Trailing 2-0 following superb first-half goals from Italy striker Simone Zaza and Nicola Sansone, Icardi struck seven minutes from time to give Roberto Mancini's side hope of snatching a late draw.
However, the striker's goal celebrations fell resoundingly flat.
Icardi took off his shirt and after a flashy jump over the advertising hoardings, threw it into a section of Inter fans.
Perhaps hoping for a more positive reaction, Icardi was left red-faced as irate fans of the struggling Serie A giants promptly threw it back.
As Icardi stood stunned, Colombian teammate Fredy Guarin ran to the rescue in a bid to rally the fans to Icardi's cause. All to no avail. As fans rained down whistles and insults, Icardi lost his cool and shot back insults of his own.
Inter's woes deepened when Sassuolo took their lead to 3-1 in injury-time when Domenico Berardi slotted a penalty past Inter 'keeper Samir Handanovic.
Icardi tried to repair the damage with fans after the game when, accompanied by Andrea Ranocchia, Juan Pablo Carrizo, Samir Handanovic and Rodrigo Palacio, he went back out to the group of supporters to offer his apologies.
Mancini later told reporters: “Sometimes there are disagreements between the fans and the team, but I hope it has been resolved because we need our supporters.”