Arthur, a South African and the first non-Australian to coach the team, who had a contract until 2015, is pursuing legal action over his dismissal.
Slater believes the whole affair, with Darren Lehmann coming in to replace Arthur, has disrupted the Australian dressing room.
"They don't have that instinct and belief in themselves," Slater said. "I honestly feel that the axing of Mickey Arthur has weighed pretty heavily on a few of the individuals in that playing group.
"They are now trying to adjust to a very positive, very good man-manager in Darren Lehmann but this is his first taste of international coaching."
Slater, however, insists the display in the second Test, in which the tourists were bowled out for 128 in the first innings, was unacceptable.
"They get paid a fortune to do what they do and they are underachieving," said Slater, speaking on BBC Radio 5 Live's Sportsweek programme.
"The batsmen, one to six, it's just not good enough. They have lost the ability to build an innings, to understand what is required when they get to the crease. They swan around and do their thing and we want more from them.
"I think they are trying too hard. It's about what is between the ears, being confident, letting natural instinct run. You start thinking too much of the consequences and the headlines. It's a vicious cycle. As much as you learn how to win you also learn how to lose."
There was more bad news for the Australians from former England captain Mike Gatting, who believes they could suffer a 10-0 whitewash in the back-to-back Ashes series.
Gatting said: "I've been very disappointed. They just haven't performed at all. There doesn't seem to be any game plan. They don't seem to be here to really fight hard. It's a shame because the bowlers have done a great job so far."
Asked if a whitewash was possible he added: "The way the Australians are playing at the moment you would have to say yes, but I can't see them playing this badly all the way through. If they do then they are going to get beaten 5-0.
"If they keep performing like this then it could well be 10-0. It's up to the players to go out there and fight. There doesn't seem to be any of that. It seems to be all over the place at the moment."
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- Darren Lehmann