Alli went down in the box under pressure from Kyle Naughton late in the first half, with Harry Kane converting from the spot to send the hosts on the path to victory at White Hart Lane.
Pochettino rejected the notion that English football is different to the rest of the world when it comes to player simulation, pointing to Michael Owen winning a penalty against him back at the 2002 World Cup when England met Argentina.
"It's too difficult to advise because you cannot recreate in the future the same situation and you cannot advise, 'Don't fall down or...' - it's too difficult," Pochettino told reporters.
"It's too difficult to work like that. Dele is how he is. I didn't talk with him and I need to speak with him to know what happened in that situation.
"Maybe he will say, 'OK I fell down but I didn't mean to dive but the referee believed it was a penalty', or it wasn't his intention, but it's difficult now.
"It was 15 years ago when Owen dived. Don't believe that English football is fair play always because Owen jumped like he was in a swimming pool. Come on. I didn't touch him. I promise you. It's true.
"I think today football is more global. England is more like European football. Now we have the influence of the Latin people that try to cheat always.
"Maybe you were more pure 20, 25, 30 years ago. Now you are like us."
Pochettino has experienced situations where players practiced diving in Argentina, but would never advocate that as a head coach.
"In Argentina, yes the people sometimes practise that," he said. "It's true, but many years ago. Now, I don't know. But when I was a player, it was part of training to try to cheat. Yes, [it was] at Newell's, Estudiantes, it was part of practice.
"No [I don't practise with my teams], of course not. I don't like. I don't like that."