The defender appeared at fault for Swansea's go-ahead goal in the 62nd minute at the Liberty Stadium when Leroy Fer appeared to win the ball off him before bundling beyond Thibaut Courtois.
However, a closer look at the incident shows that Cahill was indeed fouled by Fer in the lead-up and the goal should never have stood.
The England international took to Twitter to display his anger by posting a clip of the tackle which ended with Cahill glaring at referee Andre Marriner, accompanied by the message 'Incredible' and nine angry red faces.
Cahill later deleted the Tweet and it is understood that he faces no charge from the FA for his actions.
He did, however, tell BBC Sport: "It was a clear foul. I'm frustrated. I went over to him [Marriner] at the time.
"I criticise myself but come on, seriously. The most worrying thing for me - and I've just been to see him now - is there's no two ways.
"You could be sat on the moon, on top of the stand, anywhere in the stadium, you can see it's a clear foul.
"I felt the foul clear as day on the pitch and seeing it back it just made me more angry."