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Sutherland added that he was prepared to meet with Warne and discuss the 43-year-old's criticism of CA's player rotation policy and his claim that "rubbish" decisions were turning Australian cricket into a "big joke".
After venting his initial anger on Monday, Warne reiterated his views a day later.
"As I said last night we need cricket people running the team & who understand cricket & what's required at the top level, not muppets," he tweeted on Tuesday.
Warne questioned the logic of having former rugby union international Pat Howard as the board's high performance manager but Sutherland threw his weight behind the former Wallaby back.
"I have every confidence in Pat Howard and his team, and what they're doing," Sutherland told local media on Tuesday.
"Personally I find it a little bit disappointing to read about that (Warne's criticisms) in the fashion that I have.
"Ideally you'd like to be able to sit down with Shane and understand a little bit more deeply his opinions."
Australia won all three Tests in a recent series against Sri Lanka but were held 2-2 in the subsequent one-day internationals after resting skipper Michael Clarke for the first two matches.
The hosts, however, lost both Twenty20 internationals and were left debating the merits of a controversial rotation policy CA has introduced to manage injuries and the workload of their frontline players.
While Warne insisted Australia needed to field their best 11 players every time they stepped out, fast bowling great Dennis Lillee has backed CA's approach.
"He's 100 percent in agreement with the selection panel with managing the load and development of players," Sutherland said of Lillee, who captured 355 wickets in 70 Tests.
"Who's right here?
"You've got Shane Warne saying one thing, Dennis Lillee saying another. It's not a black and white issue."
Warne retired from Test cricket in 2007 after taking 708 wickets in 145 Tests.
