The Ghana and Chelsea star was ruled out on Thursday when he failed a fitness test on a knee injury he picked up while training during the CAF Africa Cup of Nations in Angola last January.
Australia will face the African side on 19 June in Rustenburg but Cahill, who scored twice as a substitute against Japan at the 2006 FIFA World Cup, believes they will still represent a tough challenge.
"It means nothing - we just have to work hard and concentrate on us," he said. "Essien is a big player and it is sad for him and his family not to be involved in such a big competition, but we just have to think about our team."
Cahill scored ten goals this season for his club as they recovered from a slow start to finish eighth and just miss out on a UEFA Europa League place.
Australia coach Pim Verbeek is likely to use him in a more advanced role next month with only three other strikers named in a 28-man squad and Cahill admitted he is hoping to replicate club form for his country.
"As long as I'm consistent and I keep working hard then it should work out," he said. "Ït's fantastic to be here. South Africa is a beautiful place and we're just happy to have arrived and be training hard. This is where we want to be and hopefully come the first game we will be ready."
Cahill also admitted it was a relief to have signed a new four-year contract with Everton this month because he can devote his attention to Australia's FIFA World Cup campaign.
"I think it's important as a footballer going into such a big competition to not have big distractions like not knowing where you're going to be next season," he said.
"You need to be totally focused because that is the only way you can give 100 per cent to your national team. The big thing for me is that I'm very close to the manager and the chairman so I'm buzzing to have signed a new contract."