The Nerazzurri boss was pleased with what he saw from his new side after they drew their latest pre-season friendlyInter's "growth" following their 1-1 draw with Hamburg on Saturday.
The Nerazzurri had won all of their pre-season games prior to the encounter, but though Mauro Icardi looked to have extended their 100% record, a Artjoms Rudnevs strike brought that run to an end.
"Honestly I'm really pleased with what we did today, we were good," Mazzarri told Inter Channel after the game.
"I'm sorry that we conceded the goal we did, it was probably the only chance we gave them in the whole game. The important thing is that the team played well which wasn't easy tonight because Hamburg pressed really well.
"It is clear that there is some work to do but I'm happy to continue like this because I see progress every day."
Icardi, who joined the club from Sampdoria as part of a co-ownership deal earlier this summer, then revealed his delight at scoring his first goal for the club.
He added: "Guarin gave me a nice ball and the only thing I could do was put it away. I had not scored and it is a great satisfaction for me scoring my first goal Inter.
"We played a good game. was more difficult than we had done in Pinzolo. now my legs start to go, and we are well on the field."