The 23-year-old moved to Liverpool from RB Leipzig during the summer transfer window, and the Guinea worldwide has appeared in all four of his new team's Premier League matches this season.
On Wednesday, he was fined £50,000 and banned from driving for 20 months after admitting drink-driving.
"He is the first to regret about all that happened", Pochettino told reporters at the club's training ground ahead of Saturday's home clash with Liverpool. He doesn't feel great. "He said he is sorry and he is a man and accepts his mistake".More news: Serena said she was proud of me - Osaka
"He's punishing himself. But of course we're not God, that we can judge people. That is a massive lesson for everyone, he was the first to tell me he made a mistake". "I am disappointed because we are going to miss him for this game and maybe the Champions League game against Inter Milan [on September 18]".
The Premier League club said any disciplinary action they might take would remain an internal matter.
He added: "Lloris will have another scan to see the evolution of his injury".
Alli withdrew from the England squad for Tuesday's friendly against Switzerland after suffering a strain during the 2-1 loss to Spain on Saturday.
Liverpool will attempt to make it five straight Premier League wins at the start of the 2018-19 campaign when they travel to Tottenham Hotspur this weekend.