Lloris' injury seems to be the worse of the two as he's expected to be out several weeks.
When officers stopped the vehicle, they found vomit and said Lloris had to be helped from the auto.
'He already knew in the moment that it was a big mistake.
Pochettino said: "We are always confident we can beat any team".
"It's a massive lesson for everyone. Because he is clever he'll learn and now he is going to move on".
"Of course we had a conversation and he explained all that happened", said Pochettino. "Like a man you need to recognise your mistake".
"Only we need to try, that he understands, and how he understands that it was a mistake".
With injuries, worries about the form and freshness of striker Harry Kane, delays over the new stadium and a surprise defeat by Watford before the worldwide break, Tottenham's preparation for a game against a Liverpool side boasting a 100 percent record so far has not been ideal.
When asked whether Lloris had offered to give up the club captaincy, Pochettino said: 'He apologised to everyone.
"I am learning a lot!"
"And of course it's more complicated today to be a manager than 20 or 30 years ago".
It seems likely both Spurs' captain and Alli will miss Tuesday's Champions League Group B match at Inter Milan too.
"I'm not disappointed with him", he said.