He did not refer to specific individuals, but made his comments following a question at a press conference that referred to comments from former team-mate Shane Warne.
Warne, who retired from Test cricket last January after taking 708 wickets, and former captain Ian Chappell have recently attacked former national coach John Buchanan.
Last week Warne said Australian cricket was in danger of becoming too arrogant and labelled Buchanan as "a goose".
But Gilchrist said Sunday: "There's been a lot said in the paper today, yesterday, this week it seems.
"It (the national team) is an elite club and we've always felt a major characteristic of being in that club is to show respect.
"It just seems that some guys in retirement have lost that.
"I'm not sure why people are getting personal about things in the press ... I think we, as a group, are just getting a little bit sick of a lot of the negative comments being afforded towards us or the people involved with the cricket team."
Gilchrist said he also hopes the upcoming four-Test series against India will be played without the on-field verbal clashes that marred Australia's ill-tempered one-day tour of India last October.
The Australian series gets underway with the traditional Boxing Day Test at the Melbourne Cricket Ground.
"It will be hard-fought, they're a team that has said they want to take the challenge up to us in an aggressive manner," Gilchrist said.
"Hopefully ... the players are not going to go down the route again of getting too carried away with it.
"It all got a bit out of control in the one-day series in India.
"We're both aggressive teams, we're talented teams, and we want to play hard, aggressive cricket and not go too far with it."
Gilchrist said he was not fussed about his Test batting average of 29.95 against India, well below his career 49.27 runs.
"I didn't know that stat and it doesn't worry me -- I won't lose sleep over that tonight," he said.