With Harry Kane out injured, Alli helped shoulder the goalscoring mantle with a first-half penalty that ultimately proved to be the winning goal in a 2-1 triumph which strengthened his side's hold on second place.
The 20-year-old later filled in as a central striker after Son Heung-min was taken off, and Pochettino is confident that the England international will continue to surprise people with his all-round ability.
"I saw him at 17 years old playing at Milton Keynes as a holding midfielder against Manchester United. And I don't know, always he can surprise me," he told reporters.
"Maybe one day he can play like a goalkeeper or a full-back or a centre-back. I think it is difficult to respond to that [question] because he is a player who plays in his best position, he is a player who likes to run into the box, he is very often very clever into the box.
"In the box he looks like a striker because he is more than clever, he has made his mark. Outside the box he is playing like a midfielder. Dele Alli always can surprise and you cannot guess with him. He has an unbelievable personality and character."
Alli has now scored 14 Premier League goals in 27 appearances this season.