The Liverpool superstar will sit out the West Africans’ first Group C fixture – which will take place at the 30 June Stadium in Cairo later this month – after picking up two yellow cards during the qualifying campaign.
Mane was booked in Senegal’s 1-0 victory against Equatorial Guinea in Malabo in November last year, with the Confederation of African Football also recording another booking in a 2-0 victory over Madagascar in March.
"His absence should not in any way bother us," Cisse said.
"Certainly the presence of Sadio is beneficial but without him we remain strong.
"CAF have decided, so we will not linger [on the subject].
"Certainly, with Sadio we would be very good, but even without him we will be very good.
“We all know that Sadio will have a good Nations Cup [but] the players around him have to raise their level. That's how we'll get there."
Senegal departed for Egypt on Saturday, having previously been at a training camp in Alicante.
The tournament will be Mane’s third Africa Cup of Nations, and he will be keen to erase the memories of the last one – he missed the decisive penalty in Senegal’s quarter-final shootout defeat to eventual champions Cameroon in 2017.
The Liverpool forward was also a muted presence as the Lions were eliminated in the group stage of the World Cup last summer, despite being drawn in an open group also containing Colombia, Poland and Japan.
Cisse expressed his displeasure with the rule that sees his star man suspended, believing bookings in qualifying should not have an impact on the main tournament.
"If we received a card in the qualifying round, I do not see the value of counting it during the final phase of the AFCON,” Cisse continued.
“CAF has decided that, but we will prove that Senegal exist without Mane."
On Sunday, the Lions meet Nigeria in Ismailia in a warm-up ahead of the Nations Cup kick-off.