The Milan club travelled to Florence hoping to produce an immediate response to their 4-1 battering at home to Cagliari in their last Serie A outing, but Mazzarri could not mastermind that outcome.
Despite a lengthy injury list that includes Marko Marin, Mario Gomez, Giuseppe Rossi and Micah Richards, among others, Vincenzo Montella's side ran out comfortable winners thanks to goals from Khouma Babacar, Juan Cuadrado and Nenad Tomovic.
Defeat sees the pressure increase on Mazzarri and, having highlighted his side's poor fitness after the Cagliari loss, he once again suggested fatigue played a major role on Sunday.
"I need to shake up the team, but I already knew we weren't in good physical shape," he told Sky Sport Italia.
"I told the lads we have to work hard over the next 15 days so we're in a different condition when we get back on to the pitch. It'll be tough, as many of them will be away on international duty.
"I have a clear view of what our problems are, which we managed to hide in the Europa League [a 2-0 win over Qarabag in midweek], but [they] emerged against Cagliari and again tonight.
"I know how this world is, that anything I say will be taken the wrong way. In the locker room all the players know what's wrong and took on their share of the responsibility.
"People claim I find excuses, so I've been through this many times before. Believe me, the less I say, the better it is.
"The important thing is the players know what I said and they are mortified at the situation."
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