Alli, who shortly before the incident had scored a superb goal, did not appear hurt by the missile and responded by gesturing the 2-0 scoreline to the crowd.
"Arsenal must be grateful to him... I think it was an amazing reaction," Pochettino told a news conference ahead of Sunday's Premier League trip to Everton.
"In another country the player will be down on the pitch and create a big problem. He was so honest, professional and behaved really well.
"Sometimes people have criticised him but it is good to praise him now... he is more mature now but still good -- he is so young. He is still learning."
Arsenal, who said they were embarrassed by the incident and have apologised to Alli and Tottenham, have identified an image of the man who threw the bottle.
Pochettino said the incident could have been worse.
"It's such a dangerous thing," Pochettino said. "There's no point when you go to enjoy a game and that happens."
"One person cannot create a mess in a club like Arsenal. Arsenal is going to take a big decision, with responsibility to fix. People have to behave and celebrate, and support your team but in the right way.
"It's not fair for Arsenal, the club, the fans to pay for one..."
Tottenham are third in the Premier League after three consecutive wins, five points behind second-placed Manchester City and six adrift of leaders Liverpool.
Despite their best-ever start to a Premier League campaign, Pochettino agreed that the title race was developing into a two-horse race -- such is the form of the two teams above them.
"City and Liverpool are at the top. They're the two big candidates to win the Premier League," Pochettino said.
"There is still a long way until the end of the season but it is normal if people consider them the two bigger candidates to win the league.
"Today, it's impossible to say if we are going to have the chance to fight for the title. The most important thing is to have the faith that we can compete."
(Reporting by Shrivathsa Sridhar in Bengaluru; editing by Martyn Herman)
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