A steward can be seen holding up the supporter's club membership following the full-time whistle after the Blues were blasted away at the Etihad.
Maurizio Sarri's side lost 6-0 against the Citizens, with Sergio Aguero netting a record-equalling 11th hat-trick in the Premier League.
While Raheem Sterling helped himself to a double, with German midfielder Ilkay Gundogan also getting in on the act.
It was the first time Chelsea have lost three away matches in the top-flight without scoring since December 1991.
The West London side have now dropped down into sixth in the table on goal difference, as fans call for the sacking of their Italian boss.
While supporters also slated Ross Barkley on social media following his horror error in the first half which led to Sergio Aguero putting Pep Guardiola's men 3-0 up.
City fans rubbed salt in the wounds of Chelsea as they sang "you need Mourinho" at the away end.
Jamie Carragher ripped into the visitors, claiming Sarri has turned the club into Arsenal after yet another disastrous performance on the road.
Chelsea will have a chance to gain revenge on City later this month when the two teams face each other in the Carabao Cup final.
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