Allardyce's side came from behind to beat the South Wales outfit and move ninth in the Premier League table in the process.
Leroy Fer fired the visitors ahead from a corner on 35 minutes, with the veteran defender allowing the Dutchman to run off him en route to tapping home the opener.
And although the Everton manager did not specifically name Williams, Allardyce did suggest that it was a 'stupid' goal to concede.
He told ESPN: "Anyone watching would've seen we were below par. We were too negative in our passing and when that happens it encourages the opposition to try shut you down.
"We then conceded stupidly off a corner by not marking our man properly. One of our lads has let him [Fer] go and allowed him to get into the box to score."
Dominic Calvert-Lewin levelled up for the resurgent Toffees on the stroke of half time, tapping home the rebound after Lukasz Fabianski saved Wayne Rooney's penalty.
Gylfi Sigurdsson then fired the hosts ahead with an exceptional curling effort in the second period, before Rooney rectified his earlier mistake and added a third from the penalty spot.
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