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Folau, who was lured back to rugby by Cheika in 2013 after a stint with the NRL, was sacked last month by Rugby Australia for making several homophobic social media posts.
A three-person panel found Folau guilty of a high-level breach of its code of conduct, ruling the 30-year-old out for the Wallabies at the upcoming Rugby World Cup in Japan.
Speaking for the first time since Folau's exit Cheika said the decision to terminate the star's multi-million dollar contract as unfortunate, but that in the end "something had to give".
"I've had a good relationship with Israel for a long time now," Cheika said.
"The only thing for me is the team has to concentrate on the game. Focus has to be on winning the next game or the World Cup or the Bledisloe Cup or the things that our fans want and the things that we want.
"Once that focus is not there completely, you have to either make the sacrifices to make that the No 1 focus.
"[It is] nothing to do with content, nothing to do with anything. It's just about the team is the most important thing and anything that can distract a team from achieving its goals, you have to deal with one way or another.
"It is unfortunate how it ended up, but something had to give in that situation."
Folau has signalled his intent to sue Rugby Australia and is set to seek up to $10 million in damages in a lawsuit that looks to prove the termination of his contract was "unlawful".
Meanwhile, reports emerged yesterday that the Brisbane Broncos had held a meeting with Folau suggesting he could be keen on a return to the NRL.
Tonga has also expressed a desire to have him qualified in time for the 2023 World Cup.
Folau last played for the Wallabies on their spring tour of Europe last November.