Genoa only occupy 11th position but have secured triumphs over Milan and five-time defending champions Juve, who are the only side to concede fewer goals than Ivan Juric's team this season.
Inter are just one point clear of this weekend's opponents, so Pioli knows his players cannot afford to take their upcoming task lightly.
"Juric has done a fantastic job this season. Genoa play with real grit and determination and they've done well against the big teams," Pioli told a pre-match press conference.
"They also have the second-best defence in Serie A. If we want to beat them, we'll need focus, clear heads and resolved.
"Winning would be a huge result in terms of our league position and for morale. We really want these three points.
"December is going to be a busy month but we have to take each game as it comes. There are still plenty of points to play for. We have to stay focused on the present."
Inter's ultras protested against the club during the 2-1 Europa League victory over Sparta Prague on Thursday, raising a banner before leaving an entire stand empty for their final continental fixture of the season.
Pioli is well aware improvements are required in order to get the supporters back onside after a dismal start to the campaign.
He added: "The fans made their feelings known and we have to accept the criticism. We won on Thursday and now we have to make sure we honour every game from here until the end of the season.
"We must work hard every day to build confidence and bring joy to our fans. You won't go very far unless every player is pulling their weight and running for the team from the first minute to the last.
"When we're not in possession, we must work hard as an organised unit."