Chelsea midfielder Essien was ruled out of the tournament in South Africa on Thursday after failing to recover from a knee injury.
"We will have to make a number of tactical adjustments because Essien is probably the best player in the world in his position and coping without him will be very difficult," Rajevac told Reuters by telephone on Friday.
"We have two warm-up games, against Netherlands in Rotterdam and Latvia in London, to work out a new set up and find the best possible solution to the problem.
"Obviously, it is a massive blow for us but it is also a huge loss for the World Cup itself because one of the event's best offers is watching the finest players perform.
"But the most important thing is that he gets back to full fitness and resumes playing because his career is more important to us than any single event."
Essien picked up the injury during the African Nations Cup in Angola in January, where the Ghanaians reached the final even though he played only 45 minutes for them.
Rajevac said several other players were battling to be fit for Ghana's World Cup Group D opener against his native Serbia in Pretoria on June 13.
"We have players nursing niggling injuries while midfielder Emmanuel Agyemang-Badu is still uncertain of recovering in time for the start of the tournament so it's a real headache.
"But we have to move on with the walking wounded and without the missing, that's our situation and we still have high hopes of doing well in the tournament because those who are available are raring to go."
Asked whether he considered giving Essien a coaching role at the World Cup, Rajevac said:
"Not really, I am sure the players would love to see him in the dugout because he is the team's inspirational player but he has a stringent rehabilitation programme."
"Of course, we will welcome him with open arms if he can make time to come to South Africa to support us."
Ghana, who reached the last 16 in the 2006 World Cup, play their other two group matches against Australia in Rustenburg on June 19 and Germany in Johannesburg on June 23.
