Mane was instrumental in the Lions of Teranga's Africa Cup of Nations win in February, but was ruled out after having surgery to reattach a tendon to the head of his right fibula having originally been named in the World Cup squad.
"Obviously it is a great shame for Sadio and a shame for the national team but we need to think about the player's safety and health," said Cisse, ahead of their Group A opener against the Netherlands.
"It's a challenge for us to be missing Sadio Mane. All coaches build their team around the best player and obviously that is the same for us.
"We hope he makes swift recovery and gets back to playing as quickly as possible but we have a strong team with experienced players and young players who are ready to rise to the challenge.
"It is difficult to replace Sadio Mane. He is an extremely important player for our team and we are determined to do what we can without him.
"We are going to have to work even harder as a team without him. When you talk about the morale, of course it affects you.
"We are not just talking about the Senegalese people here, people all over the world are saddened by what has happened.
"I've received many phone calls from many people saying how sad they were.
"He is our best player, the leader in that respect, (and) it's a big loss but we do still have a strong mentality, we are comfortable being together and I am sure we will get some good results at this World Cup."
Netherlands coach Louis van Gaal tried to sign Mane from Southampton when he was Manchester United manager but lost out to Liverpool.
He knows what a loss it will be to Senegal, although he will be without Memphis Depay for the opening game as he is still not fully fit having been troubled by a hamstring injury for the last couple of months.
"I think Mane is an extraordinary player and I wanted him as manager of Manchester United. He was at Southampton and I chased him at the time," said the Dutch boss.
"He can break open a match and Senegal will really miss him - but the same applies to us, we are missing our top scorer and king of the assists."
Van Gaal was asked about whether Virgil van Dijk - whom he described as a "truly excellent captain" - would wear the OneLove armband promoting inclusivity as England, Wales and Germany have pledged to do.
"I'm no longer going to speak about political issues. I am focusing on the coming match," he added.
"I put a full stop on these issues after we invited the migrant (workers) to watch our practice sessions and I instructed all my players to do that also."