The Italian highlighted the quality of Inter's display versus the Giallorossi and lauded Fredy Guarin for his recent performances.
Saturday's encounter proved to be a dour and bad-tempered affair as both sides created few opportunities to break the deadlock.
But Mazzarri took heart from the Nerazzurri's approach and Fredy Guarin's growing maturity, saying their ability to hold their own at the Olimpico was testament to his side's progress.
"I'm pleased with the way we played at one of the toughest grounds you can play at, along with Juventus," the coach told reporters after the match. "We're looking to build this year and I'm happy with the way the lads approached the game tonight. We came here to have a go at them. We did very well in the first half, we just needed a goal.
"Guarin has the occasional bad game but in the last few he has always provided the decisive passes. We missed them today.
"Guarin is a fantastic player but can be prone to dips in performance. He still has high's and lows, sometimes his game comes to a halt, but it has improved this year. He is an important player.
"I'm satisfied with what we've done so far. There have been lots of times when luck hasn't been on our side and we've picked up less than we deserved."
The point allows the San Siro outfit to consolidate fifth spot in Serie A, as it seeks a return to European competition for next season.