Alli scored the second goal for his side in a 2-0 win that set up a semi-final meeting with Chelsea next month, but Spurs' victory was marred by the incident.
No arrests have been made but Arsenal and the Metropolitan Police are working together on the issue, the force said in a statement provided to Omnisport.
"The Met is working with Arsenal Football Club to identify the person responsible for an incident where a bottle was thrown onto the pitch during the Arsenal v Tottenham match on Wednesday December 19," the statement said.
"There has been no arrest in relation to this specific incident. Seven people were arrested as part of the policing operation for this match for a variety of offences including possession of drugs; public order and assault on police."
England international Alli was clearly unhappy about the incident but was pushed away from the situation by Arsenal defender Sokratis Papastathopoulos.
He made light of the moment on social media following the game, posting a photograph where he is gesturing to Arsenal fans with the game's scoreline.
But Spurs boss Mauricio Pochettino was unimpressed with the incident and condemned the bottle being thrown, which opposite number Unai Emery said he did not see.
"Lucky that it wasn't a big issue. Come on, when we play a derby we hate each other in a good way, but that looks in a bad way, looking to damage an opponent," said Pochettino. "I cannot talk in general [terms] because only one stupid person made a mistake."
The incident comes after projectiles, including a banana skin, were thrown when Pierre-Emerick Aubameyang scored a penalty in Arsenal's 4-2 win over Spurs in the Premier League on December 2.