Spin has proved Australia's undoing this series, with Rashid the leading England wicket-taker with 11 dismissals and 19 together with off-spinner Moeen Ali.
Amid all the blazing hitting at Trent Bridge, Agar emerged relatively unscathed with figures of one for 70 in 10 overs.
Defeat raised fresh questions about England's ability to win one-off, winner-takes-all fixtures following last year's Champions Trophy semi-final loss to Pakistan.
Joe Root defended his underperforming senior players after his team meekly handed back the Ashes to Australia in Perth.
Australia were confident rain would not deny them the Ashes despite play being abandoned early on the fourth day of the third Test against England in Perth on Sunday.
Australian captain Steve Smith's incredible year continued as he notched his second Test double century on the third day of the third Ashes Test against England at the WACA Ground on Saturday.
The Australians are sailing to apparent victory in the first Test, just 56 runs away and with 10 wickets in hand, after restricting skipper Root to a second-innings half-century.
England are facing a big defeat to Australia on Monday's final day after they were bundled out for just 195, leaving the home side the task of scoring 170 runs to win.
The tourists were skittled out for 195 off 71.4 overs, losing their last six wickets for 82, as the Test swung Australia's way on the fourth day at the Gabba.
As England get ready for their opening tour match in Perth on Saturday, Stokes remains at home awaiting the outcome of a police probe into his involvement in a brawl outside a nightclub.
Stokes is waiting until the time is right before explaining the violent incident that cost him his place in Ashes squad.
Ex-Australian captain Waugh, at the helm in 57 Tests for 41 victories, said England will not be the same threat without Stokes.
Mitchell Starc has urged Australian fans to get stuck into England bad boy Ben Stokes if he makes the trip for Ashes.
Stokes was arrested last month on suspicion of causing actual bodily harm and suspended, along with Alex Hales, from the internationals.
Ben Stokes, whose ability with both bat and ball makes him that most highly prized of cricketers -- a genuine all-rounder.
Stokes was dropped for fourth one-day international against West Indies at The Oval after being arrested early on Monday.