First, Wanderers striker Federico Piovaccari was disallowed an opening goal after a shoulder-to-shoulder tussle with Dylan McGowan.
The pair had each other by the shirts as they hurtled downfield but the stocky Italian was stronger, driving the ball past United custodian Eugene Galekovic, who didn't even bother to dive.
If that decision was 50-50, what came moments later was clear-cut.
Michael Marrone charged into the box and was fouled by Wanderers captain Nikolai Topor-Stanley, only for Williams to ignore it.
Then, right on the tick of halftime, McGowan appeared to bring down Mark Bridge in another appeal gone wanting.
After the match, Williams admitted that after watching video replays he realised he'd gotten it wrong on the latter two counts.
"Having seen the contact now (from Topor-Stanley on Marrone), I think that's a penalty. So my apologies there," he told Fox Sports.
"In regards to the other one with the Mark Bridge challenge ... that's probably a penalty also.
"Of course, we never like to make errors, but this is the way it goes.
"From my position that's what I saw on the day."
Adelaide coach Guillermo Amor agreed Marrone should have earned a penalty, while Popovic said it was disappointing Piovaccari did not seal the winner - a decision Williams was not asked about.
"The one with Nikolai, you see those given. The one with Bridgey, that was a pen," he said.
"But the one with Nikolai happened just after Piovaccari's goal was disallowed, so that wouldn't have happened.
"I think getting that first one wrong was a shame, because they were both pulling each other."
The Wanderers pressed hard and looked like they would score right up until the final whistle, in a dominant second half when Adelaide finally ran out of puff.
Bruce Djite had the earliest shot at opening the scoring, however Wanderers gloveman Andrew Redmayne was quick to stop it, as he did in a fine reflex move late on to deny Craig Goodwin at the near post.
Sergio Cirio came even closer to joy with a lovely strike off a Djite cross that hit the woodwork.
Western Sydney too had their chances.
Classy United custodian and skipper Eugene Galekovic reached high to tip an audacious chip from Andreu over the crossbar, then dived left to stop Castelen's on-target belter.
Piovaccari had sore luck all night, including when his solid header was unwittingly deflected by an offside Bridge before it reached its destination at the goal's bottom corner.
AAP ek/gc
-AAP
