The Grifoni began the season with two defeats but an inspired performance saw them brush aside Samp 3-0 last Sunday.
"The result against Samp was divine in a special game," Liverani said. "Our approach to the derby was exceptional and I ask my players to show the same determination in every game.
"Our fans can continue to enjoy our derby win but we have to now focus on our next task which is Livorno."
Liverani knows his team cannot get carried away as they face a stern test on Saturday against the promoted outfit.
"Livorno have enjoyed a strong start to the campaign," he said. "It's not going to be easy to get a result but we will go out determined to get three points."
Rivals Livorno won 2-0 at home to Catania last time out.
That result followed their 4-1 triumph at Sassuolo and kept the Tuscan outfit in the top half of the standings.
"We are satisfied and calm," Livorno coach Davide Nicola said. "We are aware that there is still a long way to go.
"The team is playing well and this is a good sign.
"We have adapted well to returning to Serie A and we hope we can continue to do well."
The visitors are without Brazilian defender Emerson, who is out with a muscular injury.
Livorno fans had hoped new signing Miguel Borja would make his Serie A debut at the Luigi Ferraris stadium.
However, the Colombian striker will not feature this weekend as he has yet to receive his work permit to play in Italy.