A breathalyser test on the scene found Lloris to have been over twice the drink drive limit.
Lloris missed Tottenham's last game against Watford after sustaining a thigh injury, with Michel Vorm drafted in to deputise in his absence during the 2-1 defeat at Vicarage Road. "Of course, he doesn't feel great". He said he was guilty of this situation and it's irresponsible.
"But I think everyone can make a mistake".
'He is punishing himself. But of course we're not God, that we can judge people.
"Everyone can make a mistake, he made a mistake and he is suffering". It's a massive lesson for everyone. I want a watch or some Korean food.' Because when we see in the past that different clubs didn't allow [him] to go to play in this tournament, who took the risk? "Now I need to pay like a man".
"I'm not disappointed with him", he said.
When asked whether Lloris had offered to give up the club captaincy, Pochettino said: 'He apologised to everyone. "That is a massive lesson for everyone, he was the first to tell me he made a mistake".
Pochettino said: "He already knew that it was a big mistake". He was lucky there was no effect. "Now, because he is clever, he learns and he is going to move on".
For Pochettino, it is the latest in a series of complications at the beginning of this campaign.
"He is a man and he is very conscious about what happened, and of course you can not remove it, but he has the capacity to move on, learn and be focused on playing football", said Pochettino.
Alli suffered a hamstring injury against Spain in the first-half and Tottenham are privately frustrated that the midfielder then completed the game.
"He [Alli] suffered a small injury after 20 minutes of the game against Spain at Wembley", he said.
It seems likely both Spurs' captain and Alli will miss Tuesday's Champions League Group B match at Inter Milan too.
Son gives Spurs another option in attack, while Pochettino defended Harry Kane, whose form has been criticised in a start to the season when the World Cup Golden Boot victor has seemed to lack sharpness.
The coach added: 'We have confidence and trust in him. There's no doubt that he's one of the best strikers or players in England and in Europe. It is only a matter of time before he shows his real quality.
"I told him today: 'Where is my present, Sonny?"
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