The Nerazzurri coach is already under immense pressure and the defeat to the bottom club will only see it increase
With rock-bottom Parma coming into the game, coach Roberto Donadoni was also thought to be in danger of losing his job.
However, the former Italy coach's players responded with a resolute display at the Stadio Ennio Tardini, posting their first clean sheet of the season - much to the frustration of Inter boss Mazzarri.
De Ceglie gave Parma the lead after just five minutes, before the former Juventus man wrapped a much-needed three points up with his second against the run of play after Mateo Kovacic had struck the woodwork for Inter.
Mazzarri could now face difficult questions surrounding his future after Inter's toothless performance ensured they missed the chance to move level on points with third-placed Napoli.
But Donadoni will be thrilled to see his side move off the bottom of the table ahead of Chievo's clash with Sassuolo on Sunday.
Parma made an ideal start when Andrea Rispoli crossed from the right for De Ceglie to bundle over the line.
While buoyed by their lead, Parma's strong start was dampened somewhat when Massimo Coda limped off after appearing to turn his ankle 14 minutes in.
Joel Obi's diving header was then kept out by Antonio Mirante, with the Nigerian’s effort sparking the first real spell of Inter pressure.
Mazzarri's team struggled to add to Obi's attempt on target, although they should perhaps have been awarded a free-kick on the edge of the area when Mauro Icardi appeared to be hauled down by Alessandro Lucarelli on the Parma skipper’s return from suspension.
Zdravko Kuzmanovic fired wide early in the second half before Mazzarri opted to add Brazil international Hernanes into his midfield prior to the hour mark.
The former Lazio man's introduction helped offer some attacking impetus, but clear-cut chances remained few and far between for the visitors.
Perhaps summing up Inter's below-par display, Rodrigo Palacio missed the chance to register his first league goal of the campaign when he blazed Icardi's cutback way over the crossbar before Kovacic hit the post.
De Ceglie then sealed the three points with a finish from close range that found its way through keeper Samir Handanovic's legs - leaving Mazzarri with much to ponder ahead of Inter's midweek trip to Saint-Etienne in the Europa League.