"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.
"Of course he doesn't feel great. He said he is guilty of this situation and is responsible. He made a mistake and is suffering, and is punishing himself.
"It's a massive lesson for everyone. He told me 'boss it's a massive lesson for me, I made a mistake and need to pay' and now he's accepted (it) like a man that he is."
Pochettino confirmed the 31-year-old Frenchman, who was banned for driving for 20 months and fined 50,000 pounds, would remain as the club's captain.
Lloris admitted being more than twice above the drink-drive limit when he was stopped by police in central London last month.
The Premier League club said any disciplinary action they might take would remain an internal matter.
He is currently out of action with a thigh injury sustained during his side's victory at Manchester United.
(Reporting by Martyn Herman; Editing by Toby Davis)
