As James Forrest spun away after scoring Celtic’s third goal just before half-time, Lustig tore forward to join the celebrations.
Before embracing Forrest he made a quick detour to pinch a hat from an unsuspecting policeman, placing it on his head for joining in the joy with Forrest and Tom Rogic.
He quickly handed back the hat to the copper, who appeared to see the funny side of the situation.
However, Police Scotland later issued a statement saying they were “very disappointed” with Lustig’s actions.
A spokeswoman said: “We are very disappointed with the player’s actions and have spoken to Celtic Football Club who will deal with the matter internally.
“No further action will be taken by Police Scotland in regards to this.”
A video also circulated on social media of Lustig checking his pocket to see if Rangers winger Jamie Murphy was inside while the game was still going on.