France's World Cup-winning captain Hugo Lloris avoided jail but received a 20-month driving ban and a £50,000 ($65,000) fine on Wednesday for drink-driving in central London.
A breathalyser test on the scene found Lloris to have been over twice the drink drive limit.
'Of course he doesn't feel great.
Asked whether Lloris, who was found to be twice the legal limit and had a passenger in the auto, would remain captain, Pochettino said: "Of course".
"Of course he's punishing himself. I take full responsibility for my actions, and it is not the example I wish to set".
Lloris missed the defeat at Watford before the global break after suffering the problem during the win over Manchester United in late August and the French worldwide is expected to be out for several weeks. "Like the man that he is, he's going to pay and accept everything".
'It was a mistake & then we are men & women - we can all make mistakes. Of course he's lucky there was no effect - that is important - and it is a massive lesson for him, a life lesson.More news: 9/11 anniversary: Russian bombers intercepted near Alaska by U.S. fighter jets
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His lawyer said Lloris knew he should not have been driving and had called a cab after a night out. Because he is a clever, he learns and now he is going to move on'. He's the first, he told me, "Gaffer it's a massive lesson for me".
He had not been allowed to play in the tournament by his old club Bayer Leverkusen four years ago.
Alli suffered a hamstring injury and Lloris a thigh injury.
Midfielder Moussa Sissoko will be another absentee for the Wembley meeting with Liverpool but, while Harry Winks could be in contention to start, his manager said the Englishman's ankle condition is "chronic".
It seems likely both Spurs' captain and Alli will miss Tuesday's Champions League Group B match at Inter Milan too.
"I told him today: 'Where is my present, Sonny?"