Sunday's defeat was Milan's fourth of the campaign and, with the Rossoneri having picked up just three wins from their opening nine games, Allegri is starting to feel the heat.
"We have yet to find balance in our performances," Allegri said.
"The defeat at Parma is painful because it leaves us further away from the top six positions. Now our task becomes more difficult.
"But we must believe in ourselves and take it one step at a time."
The Rossoneri lie 10th in the standings, 16 points adrift of leaders Roma and 11 behind Juventus, who are third and occupy the last Champions League qualifying spot.
Milan's main problem has been their poor form away from home, with the Rossoneri having mustered just two points from a possible 15 away from the San Siro.
"It's clear that things are not falling into place when playing on the road," Allegri said. "We certainly need to improve our performances away from home if we are to have any hope of climbing up the standings."
Lazio, meanwhile, travel to the San Siro inspired by Sunday's 2-0 triumph over Cagliari.
The result halted a run of three games without a win for the Biancoceleste and allowed coach Vladimir Petkovic to breathe a big sigh of relief.
"We have three more points and we have taken a step forward," he said.
"The team needs to remain calm and believe in the job we are doing.
"We can still do better but the important thing is that my team showed that in difficult times we can react."
The victory lifted Lazio up to seventh, three points above Milan.
The Romans have taken just one point away from home this season but will be hoping the return of striker Miroslav Klose to the starting XI will guide them to victory.
Klose came on as a second-half substitute against Cagliari and inspired his team to victory by scoring the opener.
The hosts are without defender Matias Silvestre, who sustained a thigh injury on Sunday and will sit out Milan's next two league games.