Able to supplant Sydney in the top-six after the Sky Blues drew 2-2 with Auckland earlier on Saturday, the Reds collapsed to their equal heaviest defeat of the campaign at Perth's HBF Park and made it eight games without a win.
After Adam Taggart and Trent Ostler put the hosts ahead early, an error from Josh Risdon teed up Ben Folami to halve the deficit in the 24th minute.
But rather than panic, the Glory steadied and kicked away in the second half via a brace from 18-year-old prospect Jaylan Pearman.
Top of the league as recently as late January, the Reds' failure to pick up a win in the past two months sparked the midweek announcement that Veart, in place since 2020, wouldn't return for the 2025-26 season.
"Tonight was not who we are," the coach told Paramount+.
"We were well off the pace tonight.
"The timing of the announcement could have played a part, I'm not sure.
"I feel sorry for our fans, that they had to sit through that performance tonight."
Hosting Wellington before travelling to face Brisbane and Melbourne City in their remaining three fixtures, Adelaide sit seventh, a point back of sixth-placed Sydney and a point clear of eighth-placed Macarthur, with their goal difference inferior to both.
Skipper Stefan Mauk denied that the announcement of Veart's departure had weighed the team down but didn't pull punches over their performance.
"I don't really know how to explain it," Mauk told Paramount+.
"It's not good enough; we're fighting for finals.
Referring to Veart, he added: "There's no player that doesn't want to play for him.
"I know it's hard to probably believe that after that performance, I honestly don't have words for it."
Dragging themselves off the foot of the table with the victory, it was just the third win of the Glory's season and the first time they'd won a league fixture by three goals since December of 2021.
In the last home game of their season, it also gave a stirring farewell for Pearman, with the "Prince of Perth" bound for English Championship side QPR.
"To have my breakout season here with the home fans, my hometown club and to give back to them in the last home game of the season – it's an unreal feeling," he said.
