The Hibees, who were aiming to win the trophy for the fifth time in a row, lost 2-1 to Celtic, while Spartans were beaten 3-0 by league champions Glasgow City yesterday afternoon.
Dean Gibson's Hibs side led at the interval courtesy of a stunning Rachael Boyle strike, the tenacious midfielder picking up a pass from Shannon McGregor before sending an unstoppable drive into the top corner from outside the box.
However, the Capital outfit were pegged back two minutes into the second half as Jacynta's low strike beat goalkeeper Gabby English and Charlie Wellings completed the turnaround with 11 minutes remaining as her shot went in via the crossbar.
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In the earlier kick-off Spartans and City couldn't be separated at the break after a fairly even first 45.
However, the Glasgow outfit finally grabbed the opener on the hour through Costa Rican Priscila Chinchilla's astute finish into the far corner. Hayley Lauder's close-range effort doubled City's lead just moments later and it was game over for Spartans when Chinchilla grabbed her second of the afternoon in stoppage time.
Spartans manager Debbi McCulloch was proud of her players' efforts despite coming up just short in their quest to reach the final.
"I thought in the first half we kept our shape really well and the game-plan seemed to work," she said afterwards. "But if you make a small mistake against Glasgow City in key areas then they punish you and that's what happened. They had the better chances but I don't think it was a 3-0 game.
"The attitude and the commitment the players gave us was absolutely phenomenal. We want to keep competing at the top level so that's what we ask for every week. Some players never get to play in semi-finals. We know how hard we have to work to continue that. It was a tough group to get out of but we managed to get ourselves out of it and reach a semi-final. We're disappointed not to have made the final but I couldn't be prouder of the girls."