The former Lazio midfielder was promoted from his role with the Genoa youth team when president Enrico Preziosi decided against continuing with Davide Ballardini in June and the rookie boss oversaw positive results in pre-season while shrewdly rebuilding the squad.
A 2-0 defeat at Inter Milan was not an ideal start to his first Serie A campaign, however, and he knows Genoa fans are notoriously unforgiving until the goals and victories start rolling in once again.
Before Sunday's game against Fiorentina, Liverani said: "I'm not expecting too much warmth from the fans because there ought to be some scepticism on my home debut.
"We're going up against a side that has the advantage of working together for some time, but with one or two key additions."
The Rossoblu boss is looking to recruit several new faces before the transfer window closes on September 2, with full-back Giovanni Marchese ruled out through injury until late October.
"We have time to prepare well and to take appropriate action, but until the reinforcements arrive we must be prepared to make sacrifices and give our all for the good of the team," he added.
Defender Ahmed Hegazy is unavailable for Fiorentina, who opened their season with a 2-1 win over Catania, while Mario Gomez is bidding to open his goalscoring account following a summer move from Bayern Munich.
A tired Viola side struggled to hold off the challenge of Grasshoppers on Thursday, but they booked their place in the Europa League group stages where they will meet Dnipro, Pacos de Ferreira and Romanian outfit Pandurii.
President Andrea Della Valle told La Repubblica Sport: "The team is still struggling a little bit and looks a bit out of breath but there's no cause for alarm.
"We're happy to have qualified and we are already thinking about Sunday and Genoa."