Steelers’ best chance of silverware was lost as the understrength side buckled and then collapsed at Cardiff.
Sheffield had taken a 6-2 Challenge Cup lead into the semi-final second leg.
But without the injured Armstrong, Dowd, Fretter, Franssilla and suspended Jamtin, they were run ragged losing 7-1, 7-9 on aggregate.
Devils, the team who beat Steelers in last year’s final, will now defend the cup on March 4 against Belfast Giants who beat Nottíngham Panthers 12-7 (aggregate.)
Steelers will never admit it - but they can’t have been overly optimistic of clinging on to their first leg lead - as big as it was.
They were clearly exhausted last Sunday and needed more troops than they had available to ward off the nation’s best team. Having said that, taking too many penalties, cost them, too - four of Cardiff’s goals were Power Play efforts.
Steelers were expecting the traditional early bombardment and Ervins Mustukovs had to wait just 27 seconds before making his first save.
Cardiff turned the pressure into a goal, at 6.25.
With Eric Neiley serving a tripping minor Devils executed with Sean Bentivoglio, scoring from Matt Myers and Andrew Hotham.
But when Strachan took a hooking penalty 41 seconds later, Sheffield equalised on the night with Neiley converting from Jonas Westerling.
Steelers didn’t want any part of a run and gun goal game, but they conceded again at 10.18 from Layne Ulmer.
A Liam Kirk breakaway was denied by fellow South Yorkshireman Ben Bowns and for much of the rest of the first period Sheffield were penalty killing with Mathieu Roy (twice) and Davey Phillips in the box - and that led to a robust exchange of views between coach Paul Thompson and the officials at the break.
His mood wasn’t improved when 37-year-old Canadian Ulmer quickly claimed his second.
Relentless Cardiff now had the momentum and Justin Faryna made it 4-1 on the night courtesy of a turn-over.
With just one aggregate goal between them, (7-6 in favour of Steelers) it felt like Steelers needed a Herculean effort to stay in the tie - another Welsh effort was washed out after a video review.
The last period was 45 seconds old when Paul Crowder made it 7-7 aggregate.
The dam had sprung a leak and Patrick Asselin and Bentivoglio put the home side two more goals to the good.
Neiley hit the post and Mathieu Roy the bar but there was going to be only one winner.
Coach Paul Thompson later admitted his side had been “embarrassed and humiliated.”
The players had “capitulated” in the second and third periods.