Rodri scored the winner as City beat Inter Milan 1-0 in the Champions League final.
It is the first time the Citizens have won the competition and victory over United in last week’s FA Cup final means they have secured the Treble, having won the Premier League last month.
United are the only other team in England to have achieved such a feat and defender Williams decided to remind his rivals of that fact.
After the final he wrote on Instagram: “Nobody wants sloppy seconds 😵👹👹👹.”
Williams also slammed Rio Ferdinand after the BT Sport pundit congratulated Jack Grealish and his City team-mates on their historic win.
The left-back felt Ferdinand was wrong to praise City given his allegiances to United.
He added: “@rioferdy5 Bet you don’t congratulate if you was [a] player. Keep the same morals. Two face are boring.”
Fans were split on Williams’ comments with some confused by his reaction.
One wrote: “What a clown.”
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Another added: “New contract needed. He’s a club legend.”
A third said: “What is he on about 😂”
And another commented: “So embarrassing.”