Spurs were picked apart by a ruthless Newcastle attack and were down by five goals after just 21 minutes.
This defeat, coupled with a 3-2 home loss to Bournemouth last week have seen Tottenham drop out of the top four places.
Their next two games are against Manchester United and Liverpool, and it remains to be seen where their next win will come from.
"It's very embarrassing, and the first thing is probably we should apologise to the fans who travelled and to the fans who watched the game," Lloris told Sky Sports.
"Obviously we didn't show a great face today. I think we could not match the performance of the Newcastle players. We were late in all the aspects of the game, and we completely missed the first part of the game.
"Obviously the second half is another story, but it's really painful today. It's not even about talking of tactics; it's just we couldn't fight.
"I think Newcastle just had a great performance. They were very aggressive, very offensive every time they got the ball. They were looking forward, and probably it's difficult right now to assess and analyse the performance.
"But the first thing is it was probably a lack of pride. To concede four goals in 20 minutes... On the pitch, it was something strange, like we could not react. We could not bounce back into the performance, but also Newcastle deserve a lot of credit.
"They started the game at 100 miles per hour, and they were very dynamic and knew exactly what to do with the ball and without the ball, and we were a bit late everywhere on the field in all the aspects of the game."
