The Milan-based club went into the match against the bottom team in Serie A having suffered two defeats and one draw from their opening three league games of 2014.
Diego Milito forced Alberto Frison into a good save in the 25th minute and Gonzalo Bergessio went close twice for the visitors in the second period before the Catania goalkeeper crucially saved from Rolando late on to earn a point.
And Mazzarri was left fuming by the poor atmosphere created by the home supporters.
He told Sky Sport Italia: "All week the players sensed scepticism from the fans and media. These players are not accustomed to certain pressures and felt the lack of enthusiasm in the stands, as it almost felt as if we were playing in an empty stadium.
"Unfortunately, the breakthrough incident to score didn't arrive and the lads did better when the supporters were riled up a bit by going close to a goal. The atmosphere makes a difference, as anyone who played football will know.
"Our heads are not clear and therefore we don't make the right decisions and feel the pressure when making mistakes.
"I thought the team played in a more relaxed manner in Genoa, as they seemed tense at San Siro. With the atmosphere being what it is at the moment, the squad may well play better away from home. There's no point denying that.
"Jonathan and Ricky Alvarez, for example, are not accustomed to being protagonists at this level and playing with this sort of pressure. Inter made decisions over the last two years and it will take time to gain experience.
"We could've done with a moment of magic. With two or three counter-attacks we even risked losing the game."
Inter fans from the Curva Nord section engaged in a protest against the club's executives as the team coach arrived before kick-off and Mazzarri has suggested that it would be wiser for them to conduct such behaviour after the match in future to avoid distracting his players.
He added: "If there is going to be a protest, we request it after the final whistle, because the players need the warmth from the stands during the 90 minutes."
