Mauri sustained a groin injury in his left leg in training this week and missed Thursday's 2-2 draw with Vaslui in the Europa League. The Italy international will be sidelined for at least 30 days.
Without Mauri, Lazio will be looking for their first win of the campaign on Sunday at the Stadio Olimpico.
Reja was fuming after Thursday's result and expects full concentration from his players this weekend.
"We have to understand that no game in Europe is to be taken lightly," he said. "We must show more intensity, more concentration and make the most of our chances.
"I expect an improvement in that respect on Sunday."
The Biancoceleste did begin the campaign with an encouraging 2-2 draw at AC Milan.
The Romans got goals from summer signings Djibril Cisse and Miroslav Klose in their season-opener at the San Siro and Genoa goalkeeper Sebastien Frey has warned his team-mates to keep a close eye on fellow Frenchman Cisse.
"We were team-mates in the national team," Frey said. "When he is in good condition, Djibril is a force of nature."
The Grifoni also seek their first win after last weekend's 2-2 draw with Atalanta.
Genoa president Enrico Preziosi was unimpressed by what he saw in that game.
"I ask (Genoa coach Alberto) Malesani not to make me see again a first-half display like we gave against Atalanta," Preziosi said. "Perhaps he wanted to try out something new but evidently, it didn't work."
Genoa captain Marco Rossi will sit out Sunday's game with a knee injury while Slovenia winger Valter Birsa serves a one-match ban.