Dele Alli being struck by a plastic bottle thrown from the stands at Emirates Stadium showed the north London derby rivalry "in a bad way", according to Mauricio Pochettino.
Tottenham playmaker Alli was hit in the head by the missile in the 73rd minute of the EFL Cup quarter-final clash and responded with a '2-0' gesture to nearby Arsenal supporters.
The incident comes after projectiles thrown when Pierre-Emerick Aubameyang scored a penalty in Arsenal's 4-2 win over Spurs in the Premier League on December 2 included a banana skin.
Alli set up Son Heung-min for the opening goal and sealed a 2-0 victory for Spurs with an impudent chip beyond Petr Cech in the 59th minute.
Pochettino felt the incident involving Alli showed a negative aspect of the feelings between the rival clubs.
"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."
Arsenal boss Unai Emery claimed not to witness the event but stated it is not acceptable.
This guy tonight... #COYS pic.twitter.com/LCHYi8qxw6
— Tottenham Hotspur (@SpursOfficial) December 19, 2018
Emery said: "I didn't see. I thought the atmosphere in the stadium was good. If there is a situation like that, then it is not good behaviour."
Tottenham will face Chelsea in the EFL Cup semi-finals, while holders Manchester City were drawn against League One outfit Burton Albion.
Both clubs are back in action this weekend with Arsenal taking on Burnley in the league on Saturday before two more quick-fire fixtures to close out the year, including a clash with league leaders Liverpool.
Spurs face Everton on Sunday in the league and also have face Bournemouth and Wolves before the turn of the year.