A stunning debut goal from Spanish midfielder Celia and an outstanding penalty save from Eliza Campbell could not prevent Glory from suffering a 2-1 home defeat at the hands of Newcastle Jets on Saturday evening.
The visitors hit the front in the 23rd minute through Nickoletta Flannery, before Tara Andrews doubled their advantage early in the second half.
Celia's thunderous strike duly halved the arrears and after Campbell produced a superb, one-handed block to keep out Andrews' penalty, the hosts poured forward in search of an equaliser in the latter stages.
It wasn't to be, however, as the Newcastle defence held firm to ensure that Glory's search for their first points of the season would go on.
Nonetheless, Head Coach Bobby Despotovski felt that his charges took some major strides forward in terms of their overall performance.
"It was a 100% improvement on last week and the week before," he said.
"We created enough opportunities in this game to have got something out of it, but we weren't deadly enough in front of goal.
"We controlled the game and then there was a silly mistake, a cross and a goal and at the start of the second half, by the time we got out of the tunnel, there was a second goal.
"I was disappointed with how naive we were in that respect."
Glory began brightly, Shannon May firing over in the third minute after Leticia McKenna's corner had been cleared to the edge of the box and Caitlin Doeglas then also shooting over the bar following some intricate approach work featuring Celia and Katarina Jukic.
Moments later, Jukic and Celia combined effectively once again, this time the Spaniard dragging her shot wide of the target.
Having weathered Glory's early storm, however, the Jets managed to take the lead via a swift counter-attack.
Teigan Collister showed great pace to get away down the left and whipped in a teasing cross which was prodded home from close-range by Flannery.
Glory responded immediately by creating another two chances of their own, Morgan Andrews sending a glancing header over the bar and Celia narrowly failing to find the bottom corner from the edge of the box.
The visitors, meanwhile, continued to threaten on the break, notably when Flannery picked out Jenna Kingsley who was unable to force her close-range header home shortly before the break.
And it was Craig Deans' side who broke through again in the first minute of the second half, Andrews powering into the box, turning neatly and firing an unstoppable shot into the roof of the net.
12 minutes later, however, Glory forced their way back into the contest in spectacular style, May finding Celia who cut in from the right flank and thundered an unstoppable drive past Claire Coelho in the Newcastle goal.
As the game moved into its latter stages, the hosts were almost undone by another rapid Jets break which culminated in Flannery striking the foot of the post after racing into the box.
Glory enjoyed another let-off shortly afterwards, Campbell flying low to her left to keep out Andrews' penalty after substitute Hana Lowry had been harshly penalised for handball.
It looked as if that moment of quality from their 'keeper might inspire the women in purple to claim a deserved share of the spoils, but despite peppering the Newcastle box with crosses in the final minutes, they were ultimately unable to find a way through.
Perth Glory 1 (Celia 58') Newcastle Jets 2 (Flannery 23', Andrews 46')
Dorrien Gardens, Perth
Referee: Lara Lee
Assistant Referee 1: Josh Mannella
Assistant Referee 2: Adrien Liechti
Fourth Official: Shane Skinner
Perth Glory: 1.Eliza CAMPBELL (gk), 5.Shannon MAY, 6.Arianna ROMERO, 7.CELIA, 8.Morgan ANDREWS, 10.Julia SARDO, 11.Leticia MCKENNA (19.Hana LOWRY 66'), 13.Jamie LEE-GALE (4.Ayesha NORRIE 76'), 14.Caitlin DOEGLAS (9.Crystal THOMAS 57'), 24.Natasha RIGBY (c), 28.Katarina JUKIC
Substitutes not used: 21.Morgan AQUINO (gk)
Yellow Cards: Jukic, Romero
Red Cards: None
Newcastle Jets: 20.Claire COELHO (gk), 2.Hannah BREWER, 6.Cassidy DAVIS, 7.Gema SIMON, 9.Tara ANDREWS, 10.Libby COPUS-BROWN (31.Paige KINGSTON-HOGG 65'), 12.Tessa TAMPLIN, 17.Jenna KINGSLEY (11.Pana PETRATOS 90+2'), 18.Clare WHEELER, 19.Nicki FLANNERY (13.Lauren ALLAN 78'), 25.Teigan COLLISTER
Substitutes not used: 30.Nicole SIMONSEN (gk
Yellow Cards: Simon
Red Cards: None