Zacc was drafted in following Ciro Ferrara's dismissal and the debut was a 1-1 home draw with Lazio.
"There is a new atmosphere, everyone wants to prove to the Coach they can play and Zaccheroni is a man who really knows football," said Sissoko.
"It's true that when he arrived he found a team that was a little wiped out psychologically, but I am certain we are emerging from the crisis and will prove that in Livorno."
The former Liverpool midfielder won't be at the Stadio Picchi this weekend, as he must sit out a ban.
"Zaccheroni is a Coach of great experience, he won the Scudetto with Milan and talks to the players a great deal.
"We are working on tactics and he will certainly bring something new to the table. I expect a strong Juve against Livorno that will go out to win an important game for the future."