Giuseppe Mascara's temporary equaliser was wiped out by Massimo Gobbi and Francesco Modesto.
"Parma played their game by defending and then going on the counter whenever we made a mistake," Mazzarri told Sky Sport Italia.
"It all went their way too, as we saw with the double save and Edinson Cavani hitting the upright that it wasn't our night. We still should've been more focused, though.
"This is football and we've got to push forward trying to be sharper in attack. When an opponent defends with six men and Sergio Floccari pushes you as hard as any defender, it's not easy to create chances.
"It's also true that Ezequiel Lavezzi tends to dribble a bit too much rather than going for goal. It's his personality and perhaps a sign he still needs to complete his maturation."