Rodrigo Palacio scored the only goal of the game in the first half as Inter strengthened their aspirations of securing European football next season.
However, Inter were stretched for periods after the break and were posed problems by the visitors' striking duo of Ciro Immobile and Alessio Cerci.
Their efforts proved to no avail but Mazzarri feels there are lessons to be learned from the win, which came on the day Inter celebrated their 106th anniversary.
"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," he told Sky Sport Italia.
"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.
"Plus Erick Thohir was in the stands, so nobody can point out we haven't won with the president at San Siro!"
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