Zuma, who was promoted by Celtic at the start of 2014/15, has joined Kaizer Chiefs, while Nyatama, who was the club's top scorer in the league last term with five goals, has signed for Chiefs' biggest rivals Orlando Pirates.
Siwelele finished 12th in the league in 2016/17 as they flirted with relegation, but have since added Roggert Nyundu, Ali Bondo, Jacky Motshegwa, Victor Letsoalo, Sipho Jembula, Lucky Baloyi and Ndumiso Mabena to their roster.
Jelušic, however, admits Zuma and Nyatama's absence will be felt.
"It [losing players] is part of our job and we are sorry that they are not with us anymore but we wish them all the best," said Jelusic, whose side won the inaugural Prince Mangosuthu Legacy Cup yesterday when they defeated PSL returnees AmaZulu 1-0 in the pre-season event at Ulundi Stadium.
"But, of course, we cannot leave it like that. It is not easy to replace them immediately but we have to find a solution for it."
Phunya Sele Sele are expected to soon make a decision on former Pirates midfielder Roger Majafa, who is currently on trial at the club.