Steve Smith's team, facing a fifth straight Test defeat this year, was rolled for a record-low total of 85 against South Africa in Hobart yesterday, intensifying pressure on the players, coaching staff and selectors.
It was the fifth time in the past six years Australia had been bowled out for fewer than 100.
The latest debacle also followed the stunning first innings collapse of 10 for 86 in the first Test in Perth, which the Aussies lost by 177 runs.
Howard, whose position is also under scrutiny, fielded questions at a news conference at the Bellerive ground during the washed-out second day's play.
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"If you are looking for the players to have resilience you want the people around them to have resilience," he told reporters.
"So I expect Darren, me, (chief selector) Rod Marsh, all of us to show that exact same resilience we're expecting of the players."
-- Follow the leader --
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Howard said the Australian players should follow the lead of skipper Smith, who resisted the potent Proteas bowling attack for an unbeaten 48 while wickets tumbled around him.
He added the Australian team's current predicament was also a challenge for Lehmann, amid calls that his coaching reappointment last August was premature.
"I think he's in uncharted territory as well and this is a great chance for him to reinvent," Howard said.
"He's been contracted through past 2019, which is a huge year in the calendar, Ashes away and a World Cup back-to-back.
"We've got a young captain with a coach that's wanted to give the team and squad some stability."
Howard said he was ultimately accountable as the high performance chief for the current state of Australian cricket.
"As a team we're under the pump, as a system we're under the pump and I think Australians expect that fight and that's a fair expectation," he said.
Howard said he had not thought about his position, which is up for review.
"I am not even going to contemplate it after the (two home) Test series is done and to be fair I think it would only serve as a distraction to do that over the next couple of months," he said.
"Every time you say someone is not going to stay and you exit them straight away it doesn't respect the work they are doing at the time," Howard said.
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