The Reds were comfortable 3-1 winners at Anfield.
Afterwards, Mazzarri said: "For the preseason and for everything we did with Liverpool I think it was a great game.
"But you have to put your head on the handlebars because in August football you go from an opponent like Liverpool, with whom you have made an important game, to face a good team, but they are in Serie B.
"I know English football and I know how it works, but beyond English football, Liverpool is a team of phenomena and both the starters and reserves are all excellent players and it is no coincidence that if (Loris) Karius had not had two 'injuries' in the same match the Champions League final with Real Madrid would have been played on penalties.
"We are also aware of the results they have made in the other friendly matches before meeting us."