With just one Serie A win in their past 10 matches, 12th-placed Lazio are under pressure and Petkovic fighting for his job.
Petkovic's side were jeered off after their 0-0 UEFA Europa League draw against Trabzonspor at the Stadio Olimpico on Thursday.
The negativity is affecting Lazio, according to Petkovic, who desperately wants his team's luck to turn.
"We need optimism and clear heads to play this game," Petkovic told reporters.
"We have been too unlucky in 2013 and need to analyse what went wrong. We must take it one day at a time and give our all to win the next game.
"It is difficult to give a definitive shake-up, as this up-and-down mentality has been going on for months. There should be more positivity from everyone, including the media."
Petkovic believes it is only a matter of time before Lazio start turning their performances into much-needed points.
"This game is worth three points, just like the others. We want to win and turn what we've done recently into goals and points," the 50-year-old said.
"Livorno are a very good side who defend well, even though tomorrow I want to see a more productive Lazio.
"We need to prepare for this match by being aware of our strengths and emerging from this situation all together.
"The squad realised what they are risking and what they are going through, so it is important to all stick together."
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