After storming back from a 2-0 deficit thanks to a brace from Hiroshi Ibusuki and a goal from Nestory Irankunda, Adelaide looked on track to move to within three points of sixth-placed Western Sydney when stoppage time began in Tarneit on Tuesday.
But Connor O'Toole's 94th-minute equaliser dashed those dreams.
While a mathematical path to the A-League Men finals remains, a glum Veart admitted after the game that they were now out of reach.
He said the table doesn't lie and that his side's "soft underbelly" meant they were not good enough to be up there fighting with the other teams.
Adelaide United boss Carl Veart has pointed to an off-season squad overhaul. (Dan Himbrechts/AAP PHOTOS)
"Most of our defenders are off contract,'' Veart said.
"We'll be looking and doing what we think is best for the club going forward.
"We want to be playing finals, we want to be up there competing for silverware.
"Maybe we've got a little bit complacent with the relative success that we've had the last few years of being up there competing."
Things started badly for the Reds on Tuesday when an error from James Delianov allowed Matthew Grimaldi to open the scoring in the 19th minute, with James Donachie doubling the lead from a corner in the 34th minute.
But Ibusuki dragged them back into it with goals either side of halftime, before setting up Irankunda to grab the lead in the 62nd minute.
Needing to see out the game's final moments, Adelaide's defence was unable to clear a Ben Garuccio cross from the left that eventually bounced through for O'Toole - only on the park because of a suspected ACL injury to Khoder Kaddour - to finish.
"When it was there to stop and defend we just didn't have all the players wanting to do the same thing," Veart said.
Their finals hopes long extinguished, Western moved ahead of Perth and off the bottom of the table with the win, setting up a potentially wooden spoon-deciding clash between the two this weekend in Western Australia.
"The younger players (came in to) experience that and give us a lift," said Western boss John Aloisi.
"(Then) we got our equaliser, which we deserved - we deserve something out of that game."
