The Serie A side defeated Real Madrid on penalties in their opening International Champions Cup fixture in California on Tuesday, after a 1-1 draw.
Since winning a treble of the league title, Coppa Italia and UEFA Champions League in 2010, Inter have struggled to replicate those feats and finished fifth, 42 points adrift of winners Juventus, in Serie A last season.
Mazzarri is determined to restore Inter to past glories but stopped short of predicting what the club can achieve this term.
"At this moment of the year we can't decide on our target for next season," he said. "But it's clear that when you coach a team like Inter you want, as soon as you can, to bring the team back to where it belongs because of its history.
"We have had a good beginning during this pre-season and we have some interesting young players.
"We have started a new era at Inter and our mentality, our attitude, must be that of a team who are never satisfied and who always play to win, regardless of who our opponents are.
"If we act like this, then during the season we will discover what we can achieve."
Mazzarri praised his team for their performance against Real and also paid tribute to the Liga giants for fielding a strong starting XI.
"When two teams with such an important history play against each other, it's always key for a manager to bring out in the players that desire to win," he added. "Nobody enjoys losing in football, and that's what I told my players.
"Real Madrid win trophies every season but, despite that, in a friendly game today they showed an attitude aimed towards victory and when, during the game, it was necessary to play tough and produce some hard tackles, they did just that.
"This is an aspect of football that I believe highlights the right way to play - playing with the will to win every single game is crucial to developing a winning mentality."
