Magpies captain Jonjo Shelvey was sent off for standing on Alli's ankle four minutes into the second half with the score at 0-0, handing Spurs the chance to step up a gear and clinch a 2-0 victory.
Like Shelvey, who was banned for five games last season for racially abusing Wolves midfielder Romain Saiss, Alli has had his disciplinary problems in the past, but he kept cool and was rewarded with the opening goal.
Pochettino, who saw Ben Davies cement the win, was quick to praise the England international after the game, and has called for more of the same throughout the rest of the season.
"He was calm - that's important," Pochettino said after the win. "Last season, we talked a lot about that, how we need to behave and improve and learn.
"He's mature enough now to accept sometimes what happens on the pitch, but he is so calm, he is so brave.
"Then he scored - and he scored a great goal - and I am very pleased. He needs to improve, he is not at his best expression, but it is coming."