Team chiefs confirmed on Thursday that the Bayern Munich forward, who has scored 33 goals in 92 internationals, had lost his race to recover from a shin injury.
But Cisse is refusing to be downcast ahead of their World Cup opener on Monday against the Netherlands.
"First of all, I'm sad for the boy, for Sadio Mane, and then for the national team, but of course it's his health that counts," he said.
"Of course we won't hide the importance of Sadio Mane for the Senegalese team -- he's very important, a coach builds his team around his best players.
"But there's also a group here with experienced players, with young players ready to step up. We've had to play matches before without Sadio Mane."
Cisse said the African champions, who also face Ecuador and hosts Qatar in Group A, have "excellent young players".
"I have a lot of depth on the bench so I will be able to make good subs if someone is getting tired," he said.
Senegal have called up Moussa Ndiaye, the 20-year-old Anderlecht defender.
Krepin Diatta, 23, is one of those who could fill the void left by Mane.
"When you talk about the spirit and morale, of course it affects you. He is our best player and a leader," said the Monaco forward.
"But we are determined to do what we can without him. We are going to have to work harder individually and harder as a team.
"We still have a very strong mentality, we are comfortable being together and we are strong together."