Rodrigo Palacio struck the winner midway through the first-half.
Mazzarri said: "As we saw towards the end, a 1-0 can always see you drop points. We need to be more determined, not think about the result and focus on getting another goal. I told the players at half-time to act as if they weren't in the lead.
"We had a bit of bad luck and some final passes that didn't go as planned, but we did try to add to our tally."
But he added: "Plus Erick Thohir was in the stands, so nobody can point out we haven't won with the President at San Siro!"
For breaking stories and all the great banter like us on Facebook: facebook.com/tribalfootball