Alli, 19, was booked for a foul on Nenad Tomovic and caught the defender with a boot when he was on the ground.
Pochettino said he did not see the incident at the time, but planned to talk to the midfielder after he had watched a replay.
"We need to try to teach him," he said.
"He is a young player and he has a lot to learn about elite football."
Alli moved to Tottenham from MK Dons last year after making 62 appearances at League One level.
"It is his first season in the Premier League at Tottenham," added Pochettino.
"He came from League One, he needs to learn a lot. But I didn't see it. Some people say 'yes', say 'no', so I don't know."
Pochettino said before Thursday's last-32 first-leg tie that Tottenham are capable of challenging for success both at home and in Europe this season.
Spurs are second in the Premier League, two points behind Leicester, and are also still in the FA Cup. They face Crystal Palace in round five on Sunday.
Pochettino made six changes for the Fiorentina game, with the visitors taking the lead through Nacer Chadli's penalty before Federico Bernardeschi equalised.
It means Tottenham head into the second leg at White Hart Lane on 25 February with an away goal, and Pochettino said: "We have a strong squad to try to fight for every competition, we need to use all of the squad.
"It is not important to talk about using the squad. It is important how we compete, we have big motivation."
Tottenham boss Mauricio Pochettino says Dele Alli "has a lot to learn" after the England international appeared to kick an opponent during Thursday's 1-1 Europa League draw at Fiorentina.