Requiring a win to make the decider, WA instead endured a loss as Tasmania beat the home side by 175 runs on Tuesday.
Set an improbable 480 to win, WA had some moments but ultimately finished well short, Cameron Gannon (17) the last batsman out in the final session on day four.
Earlier, wicketkeeper Inglis turned heads with his T20-like 54 from 38 balls but no one else could match that pace.
Shaun Marsh went at a good clip (54 from 70 balls) but just as the former Test player was looking to put the foot down further he edged Lawrence Neil-Smith (2-47) through to 'keeper Tim Paine.
Sam Whiteman (24), Cameron Green (40) and Mitch Marsh (22) all chipped in, but needing almost six runs an over from the outset was always likely to be a bridge too far.
Paceman Paris, who injured an adductor on day one and didn't bowl again after claiming two early wickets, fronted in trying circumstances and made a commendable 48.
Sam Rainbird was the pick of the Tasmania bowlers with 4-67 while Jackson Bird took 3-63 including the important wicket of Inglis.
Beau Webster, who scored 135 not out in the Tigers' first innings and also grabbed 2-32 when WA responded, was man of the match.
WA missed out on what would have been a home final if they'd won but Green, who will more than likely end the competition as the leading run scorer (922 runs at 76.83), said there had been enough good moments to suggest an even better 2021-22.
"I think we had 17 hundreds this year in eight games. A lot of guys' games are in a really good space," he said.
"It was a tough four days, it definitely hurts, we put our hand up for a Shield final and it didn't happen this year, but I'm sure the boys will take a lot of confidence out of this season and we hope to give it a good nudge next year."
07 April 2021