"Looking back on it now, it's a red card," he said.
"So are we going to say that ultimately the correct decision was made? Because it was - I don't think Rhys got anything on the ball, and he was the last man.
"We made a couple of uncharacteristic mistakes tonight, individual mistakes that make it hard to execute as we planned."
Phoenix coach Darije Kalezic made his intentions clear soon after Williams was sent off, benching centre back Marco Rossi and injecting new signing Nathan Burns.
The former Socceroo played an influential role in just his second game back at Wellington since his stint in 2014-15.
"Nathan changed the game when he came in - he did exactly what I expected of him," Kalezic said.
"He was dangerous one on one and he's a smart player. I think he got six or seven shots on goal... he is a player who is proactive, not reactive."
Wellington couldn't capitalise despite being a man up, and paid the price in the 40th minute when Melbourne pounced on a combination of disorganised defending and poor keeping.
Former Phoenix favourite and All Whites striker Kosta Barbarouses found space down the right, running onto Jason Geria's through ball, bamboozling Tom Doyle then slotting home past Lewis Italiano's near post.
Kalezic boosted his midfield further in bringing on his second new signing, Serbian midfielder Matija Ljujic, after the break but the new combination again took time to settle. The equaliser finally came in the 64th minute, after Victory keeper Lawrence Thomas fumbled a stinging strike from Burns and Roy Krishna pounced to tap home.
Burns also featured in Wellington's 83rd-minute winner, drilling a low cross into the box which took a touch from Melbourne defender Mark Milligan before dribbling across the line.
Kalezic was afterwards particularly satisfied with the way his team fought back after trailing at half-time.
"After a really disappointing goal we conceded, the team showed patience, the team showed belief, the team show a unified atmosphere and great mentality to work on the Victory."
