Mane has been ruled out of the tournament after failing to recover from a fibula injury sustained while playing for club side Bayern Munich last week.
The 30-year-old was initially named in head coach Aliou Cisse's 26-man squad and was expected to miss at least Senegal's opening game against Netherlands on Monday before being announced later that he was going to miss out entirely.
"We are all sad, because we would love to see Sadio playing this World Cup and Sadio was doing everything to get ready for this World Cup," said El Hadji Diouf, a two-time African Footballer of the Year, who is Senegal's team ambassador.
"All big players want to shine in the World Cup but things can happen. We are going to work without him and we're going to do everything to make him proud.
"I think Sadio's going to be stronger when he comes back."
"Our first objective is to pass the first round and after the first round we're going to talk again together to see what we can do," Diouf added.
"I know some teams don't want to play Senegal because we have a good team [with] experienced players."
This is Senegal's third appearance at the World Cup finals after 2002 and 2018.
Mane is Senegal's all-time top scorer with 34 goals from 93 caps.
He has scored two decisive penalties for the Teranga Lions this year; the first helping them win the Africa Cup of Nations for the first time against Egypt in February and the second against the same opponents sealing their place in Qatar.
Senegal also play hosts Qatar and Ecuador in Group A.
