Paolo De Ceglie's brace was enough to end Parma's miserable run of seven Serie A defeats in a row, lifting them off the bottom of the table for at least a day.
Inter's defeat will no doubt intensify the pressure on Mazzarri, whose position has been the subject of much discussion over recent weeks after the resignation of long-serving honorary president Massimo Moratti was reported to be linked to his views on the coach's performance.
Mazzarri was without the likes of Pablo Daniel Osvaldo, Fredy Guarin, Yann M’Vila, and Danilo D’Ambrosio for the trip to Parma, and the Inter boss revealed after the game that Hernanes may have picked up a knock after coming off the bench.
The former Napoli boss explained a lack of options, as well as long-standing fitness issues over the likes of Rodrigo Palacio, has held back his side this season.
"Clearly 2-0 makes everything look bad. It's true we didn't put in the performance we wanted and conceded a goal at the first cross, which then made us lose confidence and get tense," Mazzarri told Sky Sport Italia.
"We hit the post with [Mateo] Kovacic and had a great chance with Palacio, but lately we've been struggling to score goals. We were also tired, as the same players have to keep going.
"On top of that, Palacio had a serious injury and his ankle is still not in good shape.
"We are in a difficult situation in terms of injuries. Even in the emergency, we played the last three games pretty well but again we failed that extra step.
"It was the same team that beat Sampdoria, but looking at the bench I didn't exactly have many alternatives."
