Sunday's 3-1 loss at Sassuolo - a team they beat 7-0 earlier in the campaign and by the same scoreline last season - left Inter a lowly 13th in the Serie A standings.
Mancini returned for a second spell at San Siro in November, having won three Scudetti and two Coppa Italia crowns first time around, with the team 12 points off the pace.
Inter are now a huge 24 points behind leaders Juventus following Sunday's setback, leaving the Coppa Italia and the return to UEFA Europa League action later this month as the remaining opportunities to salvage a dismal season to date.
By contrast, Coppa holders Napoli moved to within four points of second-placed Roma courtesy of a 2-1 win at Chievo last time out in Serie A- Manolo Gabbiadini opening his account for Rafael Benitez's men by grabbing the winning goal.
"He can play in four different positions in attack," Benitez told Sky Sport Italia when discussing his January buy from Sampdoria.
"He doesn't give defenders a point of reference, so it's very difficult to control him. With these attacking options now, we can deal with two or three games a week."
Gabbiadini could be joined in the Napoli attack by Marek Hamsik, who was rested against Chievo, while defender Kalidou Koulibaly is back from suspensions.
Inter's board have allowed Mancini to be active in the transfer market in order to turn their season around, with new recruits Lukas Podolski and Xherdan Shaqiri starting together in the forward line for the first time at Sassuolo.
Midfielder Marcelo Brozovic came off the bench and could be in line for a first start following his move from Dinamo Zagreb last week.
Mancini will be without Issac Donkor after the young defender's full debut ended with a late red card on Sunday, although his defence has been bolstered by Davide Santon's loan return to San Siro from Newcastle United.
Mauro Icardi and Fredy Guarin angrily remonstrated with Inter fans after the Sassuolo defeat but will be in contention for Wednesday night's match after Mancini played down the incident.
Algeria's elimination from the Africa Cup of Nations means Napoli and Inter can once again call upon Faouzi Ghoulam and Saphir Taider respectively.
Napoli drew 2-2 at Inter when the team met in the league in October, with Jose Callejon netting a brace.
