An error by Hugo Lloris, who was seriously injured while committing it, lead to Neal Maupay opening the scoring after two minutes for Graham Potter’s men, before a brace by teen Aaron Connolly saw off Spurs.
Despite the result the Argentine manager is not scared of being sacked, though he accepts criticism is justified.
"No, I am not worried, what worries me is life, not football," he said. "I don't want you to take it the wrong way, what scares me is life, not football.
“Football is to be strong and be brave and take decisions and to show your face when things are not good.
"That is what we are going to do, face the negative things and try to work hard to change this dynamic. In my position I need to accept all the criticism. The same when you praise me or the team.
"I'm going to accept it in the same way and it's not going to change my vision, from you or the pundit because you're criticising me or describing a situation differently to what you expect."
Spurs captain Lloris was given oxygen before being carried from the pitch with a serious arm injury after gifting Brighton the lead.
"I think the news is not good," Pochettino said of the France international, who was taken to hospital.
"We have to wait, the club is going to explain the real situation. Everyone saw on the pitch when he landed that it wasn't a good situation."
He added: "Of course it affected the game. We cannot take the credit from Brighton, but the team suffered a massive impact from that action.
"We tried to find a different way to play in the second half and we didn't have much luck.
"At 3-0 you could see the game was over. I want to say sorry to the fans and thank them for their massive effort."