Mancini, who only replaced Walter Mazzarri at Inter in November, has now overseen three successive defeats in all competitions.
Things looked to be on the up at Inter after the acquisitions of Xherdan Shaqiri and Lukas Podolski in the January transfer window but league defeats to Torino and Sassuolo have led to questions about Mancini's suitability.
Inter now sit 13th in the Serie A table, already 13 points off an unlikely UEFA Champions League berth, and a whopping 24 behind three-time defending champions, and leaders, Juventus.
The ex-Manchester City coach, who led Inter from 2004 to 2008, saw his side bundled out of the Coppa Italia quarter-finals by Napoli on Wednesday.
Inter defended manfully but in truth were on the back foot for the majority of the encounter in Naples.
And Gonzalo Higuain's excellent stoppage-time finish saw their elimination confirmed, meaning Inter's only realistic hopes of silverware are in the UEFA Europa League.
Brazilian midfielder Hernanes is convinced Inter's luck will turn, though, and was insistent the season could still be a success after the Napoli defeat.
Hernanes told Inter's official website: "I can't believe how little reward we're getting for all the work we're putting in.
"But I still think we can do something this season.
"Mancini has changed the way we play, our mentality. He wants us to press the opposition high up the pitch and play the ball.
"Results aren't going our way right now but we can still have our say in things this year."
The arrival of Podolski was meant to boost Inter's strike force but the Germany international has not scored in his six games in all competitions.
Inter desperately need someone to help Mauro Icardi, with the Argentinian responsible for more than a third of their league goals this season.
Icardi has 11 Serie A strikes - just as many as compatriot and Palermo forward Paulo Dybala.
Dybala, 21, scored in Palermo's 2-1 win over Verona on Sunday and has four in as many matches in 2015.
While Inter will still be favourites, given the talent at Mancini's disposal and their home ground status, Palermo do sit seventh - six places and four points above their opponents.
They have lost just one of their last 13 league matches - a 2-0 reverse at Juventus - which was also the last time they failed to score.
Palermo hold a good record against Inter in recent times as well, losing just one of their last five clashes.
Of those five, two have ended in Palermo home wins, but the meeting at Stadio Renzo Barbera earlier this season was a 1-1 draw after Mateo Kovacic cancelled out Franco Vazquez's early effort.
