Burley took three points from the opening two games of the season but parted company with the club amid suggestions he failed to strike up a working relationship with Apollon's sporting director.
President Nikos Kirzis told the Daily Record: "If you know football in Cyprus then this would not come as a surprise. The decision was mutual because the results were not expected. We lost our last game.
"I have no complaints about him because we had a good relationship.
"Yes, there have been some rumours but that’s because Cyprus is a small island. Things get out of proportion and you can quote me on that. But it was a decision made by mutual consent and we wish George all the best.
"He was only in charge for two official games but we had many friendlies. It has happened quickly but you have to keep in mind we also have a sporting director in charge of monitoring the team. He is from Argentina and has a different philosophy.
"The sporting director wanted one style of play but the coach had different ideas. That was the biggest problem. The men couldn’t get along with each other."
Burley enjoyed great success when Ipswich manager, taking the club into Europe by virtue of a fifth-placed finish in the 2000-01 season as he was named Manager of the Year.
He lasted only 14 games as Scotland manager, winning just three.