Tottenham manager Mauricio Pochettino said stripping goalkeeper Hugo Lloris of the captaincy was "never considered" an option.
The Frenchman was stopped by police in London in the early hours of Friday morning and charged with drink driving.
He played in Spurs' 3-0 Premier League win at Manchester United 48 hours later.
The World Cup winner has "wholeheartedly" apologised for drink-driving, saying it was "completely unacceptable".
Lloris was released on bail and is due to appear in Court on the 11th of September.
Pochettino says the behaviour is out of character and as such so no reason to punish the keeper by dropping him from the team:
"No, I never considered that", the Spurs boss said in the wake of the comfortable win over Man United.
"What happened, I was in contact with him, such a bad experience for him. He feels so sorry. He apologised to everyone, but not only apologised to our fans, us, the club and I think he shows his regret and apologised to the whole country, because that responsibility is massive.
"I think it was a good lesson for everyone, a massive lesson. He’s punishing himself. He feels so sorry and so bad because he knows that he made a big mistake, but in the same way I think he’s a man out of character.
"We are going to, of course, support him but knowing that we cannot justify of course. There’s no sense to take some decision like you told me.”