The 22-year-old was hit near the touchline as Arsenal prepared to take a throw-in during the second half at Emirates Stadium.
He reacted with a 2-0 gesture to fans – referencing the scoreline at the time.
Alli had earlier scored the second goal and Spurs went on to reach the semi-finals with a 2-0 victory.
Wednesday’s incident follows a banana skin being thrown towards Arsenal striker Pierre-Emerick Aubameyang in the Premier League match between the sides at the same venue on 2 December.
The Spurs fan responsible was fined and banned from football for four years on Tuesday.
BBC Radio 5 live pundit Dion Dublin, who was co-commentating on the game, said: “It’s sad to see. It’s mindless. Why would you do that?
“It must have had water or something in it to reach Dele Alli. Why would you risk being idiots?
“Just support your club, don’t do ridiculous things like that.”
When asked about the incident after the game, Alli told Sky Sports: “It is what it is. It made the goal a bit sweeter and the win.”