Australia is the top-ranked Test nation and successfully defended the World Cup in South Africa in March before winning the Test and one-day series in the West Indies.
The tourists also won a world record 21 consecutive one-day internationals before losing two to the Windies.
"That has given me concern for some time," Gray said of Australia's dominance.
"On many occasions I have put it to the Australian Cricket Board that they are living in a fool's paradise," Gray added in an interview with The Australian newspaper.
"Their team is the best team in the world undoubtedly, they're financially secure, their administration is at least equal to the best in the world.
"It is very easy in Australia to have a rosy view of cricket and not realise the problems internationally. It is a very serious problem.
"One of the greatest challenges cricket has is to ensure that there is a greater evenness within the competition."
Australia will host the struggling Zimbabwe and Bangladesh for Test series later this year where one-sided results are expected to do little to further the game globally.
Gray, an Australian who lives in Melbourne, said Australia's dominance had even angered some of their own fans.
The ill-tempered clash between pace bowler Glenn McGrath and West Indies batsman Ramnaresh Sarwan in the fourth Test in Antigua earlier this month had also caused resentment among Australia's sporting public, Gray said.
"In this case this was the first time the Australian public and press had taken such a strong position of opposition to the team," Gray said.
"Previously the Australian public has loved the Australian team playing so well and winning everything.
"However, I maintain that eventually the Australian public will tire of that and we may be on the cusp."
Gray, 63, will retire as ICC president in June.
