The Gunners are analysing CCTV footage in a bid to identify the supporter who launched the missile at Alli in the second half of Spurs' 2-0 quarter-final win at the Emirates Stadium.
It came not long after the England international scored a sublime goal to add to Son Heung-min's first-half effort as Spurs set up a two-legged semi-final tie with Chelsea in January.
Alli said: "It is what it is. It made the goal a little bit sweeter and the win."
Pochettino, who on Tuesday declined the chance to distance himself from those United rumours, hopes the culprit can be caught but was keen not to tarnish the whole Arsenal fanbase.
"It was lucky that it wasn't a big issue," the Argentinian said. "For me, okay we play a derby and we hate each other in a good way but that is in a bad way when you go to damage some people or an opponent.
"I cannot talk in general because only one stupid person made a mistake. I respect the Arsenal fans, like I respect the professionals from Arsenal and I respect our fans.
"For one you cannot talk about everyone. I hope that Arsenal take responsibility and through the camera they can identify because it wasn't a problem but it can happen to be a big problem."