The Grifoni, currently 10th in Serie A, have clinched just one win in their last five games.
Genoa were held to a goalless draw by Lazio on Thursday in their first game of 2011 and Ballardini is desperate for his side to return to winning ways.
"We need to find something extra, some fury or some competitive ruthlessness that, above all in periods when luck does not go our way, can make the difference," Ballardini said.
"We didn't show those qualities against Lazio.
"We must work on character and competitiveness.
"With this we will prepare for the match at Cesena on Sunday."
New signing Juraj Kucka will not feature.
The Slovakian midfielder joined the Italian side from Sparta Prague earlier this week but his transfer documents will not arrive until Monday.
The Grifoni parted company with veteran striker Luca Toni on Friday.
The former Italy international joined Juventus on a permanent transfer just six months after moving to Genoa.
Cesena coach Massimo Ficcadenti is set to name an unchanged side from the one that won 2-1 at Brescia in the last round.
The result marked Cesena's first Serie A win on the road since October 1990 and lifted the promoted outfit to safety.
"We played an almost perfect game," said Ficcadenti. "I am very happy for my team's performance and for the result.
"However, we should not get carried away.
"We have a lot of work left to do in order to defend our Serie A status."
Cesena will be looking to make it three wins in a row at the Dino Manuzzi stadium this weekend.
Ficcadenti's side are just three points clear of the relegation zone.