The Nerazzurri have not come out triumphant in Serie A since beating Livorno 2-0 on November 9.
Since then draws against Bologna, Sampdoria and Parma have followed.
"I believe many of these players are not accustomed to being first choice at Inter and they have started to feel the responsibility of that," Mazzarri told Gazzetta dello Sport. "These players are not used to having the pressure of being expected to win every time."
Parma led 1-0 after 11 minutes and Inter were made to work to earn a point in Milan.
"We had a terrible start against Parma and we took 15 minutes to wake up," Mazzarri said. "We must reflect on how we deal with certain moments of a match, as we often go too deep when taking the lead and end up conceding a goal.
"We dropped two points against Sampdoria, while against Parma, it was a balanced match and anything could have happened.
"We could easily have lost.
"At times not losing is important when you are trying to help a young and inexperienced side to grow.
"We deserved more in other games, but probably not in this one."
Inter lie fourth in Serie A, four points adrift of Napoli and the final Champions League qualifying spot.
The Nerazzurri travel to the San Paolo stadium to face Napoli on Sunday.