The Serie A giants made it two wins from as many league games this season thanks to goals from Rodrigo Palacio, Yuto Nagatomo and Ricky Alvarez.
But while he was pleased with the win, Mazzarri said Inter still had plenty to work on – with their next league match against champions Juventus on September 15.
"We still need to improve a great deal, as we are too naïve in possession," Mazzarri told Sky Sport Italia.
"In the first half the only Catania chances were created by our mistakes. We also wasted too many opportunities when the game was still in the balance.
"Was I agitated on the touchline? I always am when I see things that aren't going well, that's my job."
In Mazzarri's 3-5-2 formation, Jonathan and Japan international Nagatomo impressed on the wings, with the former Napoli coach surprised by how quickly the Brazilian had adapted.
Mazzarri hailed his team's belief and was unwilling to be drawn into title talk so early in the campaign.
"I didn't think they'd understand so quickly what I wanted from them and especially Jonathan has improved markedly in the last 15 days," he said.
"I can also see the tension the players had from last season wash away with each victory. Winning gives you confidence and in the second half, for example, we came back out on to the pitch with more belief.
"Inter's objective is to give our best and make life difficult for everybody. I'd love to have 22 or 23 world-class players so I could challenge for every tournament, but for example at Napoli there wasn't the right squad for what was asked of me."
