Mazzarri adamant Inter were denied penalty
Roberto Donadoni's side have not won against Inter at San Siro since 1999, but claimed a 3-3 draw on Sunday.
Inter's Rodrigo Palacio and Nicola Sansone of Parma scored two goals apiece in a thrilling encounter, but Mazzarri believed his side should have been awarded a spot-kick when Ricky Alvarez was brought down by Alessandro Lucarelli.
"I saw it from the touchline and it seemed like a clear penalty," he said. "I've seen much softer fouls than that given this season.
"These things don't usually get given to us, so what can we do? One day an official might give us a spot-kick by accident."
Mazzarri also suggested his players struggled under pressure against Parma, and acknowledged the visitors deserved to take something from the game.
He added: "I believe many of these players were unaccustomed to being first choice for Inter and they have started to feel the responsibility of that. We had a terrible start and after the blow (of Parma's first goal) took 10-15 minutes to wake up.
"We must reflect on how we deal with the various moments of a match, as we often go too deep when taking the lead and drop points by the wayside.
"We dropped two points against Sampdoria, while tonight it was a balanced encounter and anything could've happened.
"We could easily have lost. At times not losing is important when you are trying to help a young and inexperienced team to grow. We deserved more in other games, but probably not in this one.
"When we started this season, we had to shake off the past and with a good start people started to expect certain things from this team. That is where the problem started, as the players are unaccustomed to having the pressure of being expected to win every time.
"I told the lads at half-time to go out, not think about anything, and just play our style of football. It worked, until we went 3-2 up and then we relaxed again with the usual problems."