Having won their last two one-day cup games, WA needed to beat Tasmania on Tuesday with a bonus point to book a spot in Saturday's final at the MCG against Victoria.
Queensland will now hold onto second spot and take on the Bushrangers in the decider.
WA skipper Michael Hussey won the toss and sent Tasmania into bat so that the Warriors knew exactly what score they would need off 40 overs to win with a bonus point, but that always looked decidedly unlikely when Ricky Ponting's 95 led the Tigers to 6-307 from their 50 overs.
The Warriors needed to score at 7.7 runs an over from the outset and in an attempt to get off to a flying start slumped to 5-78 with Liam Davis (28), Sam Whiteman (13), Hussey (four), John Rogers (12) and Tim Armstrong (one) all falling relatively cheaply.
However, 21-year-old Marsh was at the wicket in his first match since tearing his hamstring in WA's one-day loss to South Australia on November 17 last year.
Hilton Cartwright briefly joined up with him before he fell for 20 from 24 balls, but then debutant Ashton Turner came to the crease and he and Marsh for a brief moment gave the Warriors some hope of what was becoming a near impossible task.
The pair put on a partnership of 86 in just 75 balls before Turner fell for a swashbuckling 51 from 43 balls with six fours and two sixes.
Marsh continued on, though, and brought up his maiden one-day century for WA before falling for 104 to a brilliant direct hit run out from Ponting who was near the circle at backward point. That ended Marsh's knock on 104 from 96 balls with six boundaries and five clean sixes.
However, with the bonus point win and place in the final gone, WA went on to be bowled out for 256 to lose the match and finish the one-day season on the bottom of the table.
Faulkner took 3-62 for Tasmania with Evan Gulbis claiming 2-57, Timm van der Gugten 2-44, Ben Laughlin 1-37 and Harry Allanby 1-50 in a solid bowling display against some big hitting.
Earlier, Ponting made 95 for Tasmania from 105 balls with 13 boundaries after being dropped twice when on four and 35.
He was run out due to a bad call from Jordan Silk who went onto bat well himself making 66 from 66 balls and James Faulkner remained not out on 59 from 37.
Marsh was disappointed to not lead WA to the bonus point win to book a spot in the final, but was delighted to score his maiden one-day century after three months out injured.
"It was obviously good to come back like that and it was just a shame that we lost that way," Marsh said.
"We dropped a couple of chances and we learnt today that you can't really drop Ricky Ponting on four and 35. On a personal note, it's a good reward for my hard work and rehab though."
Faulkner had a terrific day with the bat and ball for Tasmania, but was even more impressed with the batting form of Ponting and Silk, and then with the whole bowling unit to get the win.
"Any time you start with either the bat or ball I think it gives you confidence naturally, and it was good to be part of it but it was set up by Punter's 90-odd and I thought Jordan Silk batted really well in his second game," Faulkner said.
"We obviously knew they were going to come hard and try to get the runs in the 40 overs, but for us it was just about concentrating on what we do well and we did that by creating opportunities in the first 20-odd overs. It was good to get a win today with a solid effort."