The 22-year-old was struck near the touchline since Arsenal prepared to take a throw in throughout the second half of Emirates Stadium.
Arsenal have told BBC Sport they have been already examining CCTV to find the man who threw the jar.
Alli had earlier scored the next goal and Spurs proceeded to reach the semi-finals having a 2-0 victory.
The Spurs fan responsible was fined and banned from football for a long time on Tuesday.
BBC Radio 5 live pund-it Dion Dublin, who was simply co-commentating on the match, said:”It is sad to see. It’s idiotic. Why would you do this?
“It must have had something or water inside it to achieve Dele Alli. Why could you risk being idiots?
“Only encourage your club, don’t do ridiculous things like this.”
When asked about the incident after the match, Alli told Sky Sports:”It’s what it is. It made the goal a bit sweeter and the triumph “