Moores was dismissed on Saturday shortly after Andrew Strauss was appointed England’s director of cricket, though reports of his sacking were leaked during the team’s washed-out one-dayer against Ireland on Friday.
Moores, who also spent two year as coach between 2007 and 2009, bore the brunt of criticism for a dismal World Cup, in which England failed to progress from the group stages, and the drawn test series against the West Indies.
“The fact that all these leaks came out the day before the man was officially told — you’ve got to show a bit of respect to employees,” Stewart, England’s most capped test cricketer, told the BBC.
England assistant coach Paul Farbrace will take charge for the two-test series against New Zealand which begins on May 21 but Stewart said appointing a permanent successor quickly was vital.
“There are a couple of names being bandied about, both Australians, Jason Gillespie, Justin Langer.
“They’ve either got someone lined up already, to have made this decision, or they’re going to have to find someone pretty quick.”
Stewart was also touted as a possible candidate for the director of England cricket role but said the appointment of former captain Strauss was an astute move ahead of the Ashes series starting on July 8.
“He’s captained his country and when you’re captain you make bold decisions, you make brave decisions, you make decisions you believe in,” Stewart said.
“I don’t take it that Andrew Strauss is a ‘yes’ man or he’s too close to that dressing room. If he has to be cut-throat then he will be.
“It’s going to be tough. Australia are the best side in the world. They’re going to start as the underdogs, but the underdogs do sometimes win.”
Former England captain Michael Vaughan said the dismissal of Moores, who won 19 of his 52 matches in charge across all formats of the game, was “disgraceful”, adding that the ECB needed to demonstrate some “quiet authority and integrity”.
(Reporting by Tom Hayward, editing by Ed Osmond)