Darren Lehmann's men dismissed their hosts for 361 in the morning session but failed to launch a substantial reply and were quickly donning their fielding whites again after lasting just 53.3 overs out in the middle.
Peter Siddle gave the Baggy Greens a timely boost by snaring a trio of quick scalps at the start of England's second knock, leaving Alastair Cook's men 31-3 at stumps, but Australia lie 264 runs in arrears at the end of a day in which 16 wickets tumbled.
And Warne says some of his country's stroke-makers - in particular Phil Hughes, who wafted at a Tim Bresnan delivery and was caught behind by Matt Prior, and the recalled Usman Khawaja, who was pouched by Kevin Pietersen after hitting Graeme Swann down the ground - gave their wickets away.
"The Australian players will be really disappointed with the way they got out," the ex-spinner told Sky Sports Ashes HD. "They will be hurting and feel like they've let themselves and the team down.
"England bowled well but Australia are better than some of the shots they played and all out 120-odd is nowhere near what they should have got.
"Hughes was looking to be positive and aggressive but his shot was a bit loose and he hadn't really judged the pace and conditions, and after losing a couple of wickets, Australia needed someone to be tight, spend some time and rebuild.
"Plus, there was no conviction from Khawaja after he got tied down by some bowling from Swann; it was not a big hit down the ground, it was a little chip."
Warne, though, reckons Siddle's late show has given Australia "hope" that they can pull off a miraculous victory and level the series at 1-1 ahead of the third Test at Old Trafford, which begins on Thursday, August 1.
But Sir Ian Botham was less than complimentary about the Antipodeans' bowling to England in the first session of the day when Swann and Stuart Broad put together a rapid-fire last-wicket stand of 48 to lift the home side past 350.
And, following the way Ashton Agar and James Pattinson flourished with the bat in the first Test at Trent Bridge, the one-time all-rounder feels both teams have forgotten how to get rid of lower-order players.
Warne said: "Australia needed [Siddle's intervention] after what had been a pretty horrendous day and to keep Cook, [Jonathan] Trott, and Pietersen, who haven't got a lot of runs in the series, down was a positive.
"At 31-3 Australia will now think 'if we can bowl England out for something like we made we are still in the game'. England are way ahead but Australia are hanging onto hope and if they bowl like they did in the evening session there might be an upset."
Beefy added: "I find it quite strange that bowlers change their tactics to tail-enders; England were guilty of it at Trent Bridge and got carted around and Australia were guilty of it today (Friday).
"They went for a bang-in theory and while a few good-length balls got hammered, almost half of the deliveries to Broad and Swann (49 per cent) were short and they got pulled and hooked out of the ground.
"Why are you changing your tactics when you are bowling at numbers 10 and 11 when the top six batsmen are getting out to good or full-length stuff? I don't understand it.
"You should bang in a couple straightaway to get the tail-enders back, but then try and bowl them out when they're not so keen to come forward."