Following their dramatic 2-1 defeat to Atalanta on Sunday, Inter were held to a goalless draw against Udinese on Thursday.
While in Sunday's defeat, Inter had plenty of chances to pick up the victory needed to boost their hopes of European football, the stalemate against Francesco Guidolin's men was a more dour affair.
It leaves Inter in the final UEFA Europa League place, but they remain vulnerable as Parma have played a game less and Mazzarri feels the club's rivals may benefit from gaining a tougher edge.
"When we consider these two results we deserve many more points than what we got out of them. It could be that we aren't cynical enough, I don't know," he said.
"But I believe that we can advance well by following this path.
"What mattered was winning and the team tried everything they could. We deserved to get three points, as was the case against Atalanta."
With Mazzarri approaching the end of his first campaign at San Siro, the Italian is preparing for what could be a decisive close-season in terms of transfers with president Erick Thohir apparently eager to splash the cash.
Manchester United Nemanja Vidic has already agreed to join, while a host of other big names have also been linked with a move.
And Mazzarri thinks his existing squad must understand the privilege of playing for Inter.
"This season as a coach I have to get the team to play well, to create, and to get the less experienced players to make progress," he added.
"To get them to understand what it means to be an Inter player.
"In June we'll make choices based on the kind of strength the club would like to project. We'll make the right choices to make my second year here start out in the right way."
