The Chelsea midfielder was yesterday ruled out of the finals in South Africa after it was discovered that a knee injury suffered at the African Nations Cup in January is taking longer to heal than initially anticipated.
His absence is a major blow for the Black Stars and their Serb coach, who told the Ghana Football Association (GFA) website: "I am really disappointed that Michael Essien will not be at the World Cup for Ghana as a player.
"He is an important player on and off the field but we can't use him this time. Essien brings lots of advantages. He brings so many things to the team and always gives us options. It's most unfortunate."
Essien, 27, missed a large part of the recently-concluded season due to the same knee problem as well as an ankle injury and has hardly played any competitive football since December.
He is not the only player in Ghanaian squad that had been struggling with injury - defender John Mensah and midfielder Emmanuel Agyemang-Badu are also major concerns for the west Africans. The pair sat out training yesterday and are on "a light training programme", according to the GFA.
With Essien now out of the picture, Rajevac is desperate for the other players in his squad to stand up and be counted.
He added: "I hope and believe that the other players would give off their best. We want to achieve with this team and must work hard. We will focus on the task ahead and hope we have a good World Cup. I hope the past experiences with injuries, though unfortunate will help us stay united and fight for each other."
Ghana, who are making a second appearance at the FIFA World Cup following their debut four years ago, are in Group D for the finals, alongside Germany, Serbia and Australia.
They play two friendly games against the Netherlands in Rotterdam on 1 June and against Latvia in Milton Keynes on 5 June, before flying out to South Africa a day later.