Tottenham could have moved level on points with Newcastle with a win but conceded five goals in the opening 21 minutes, eventually losing 6-1 at St James' Park.
Many of the Tottenham fans who had made the long trip to Tyneside were seen leaving before half time.
"It's very embarrassing. We should apologise to the fans. We didn't show a good face and we could not match the performance of the Newcastle players," Lloris, who was substituted at half time, told Sky Sports.
"We were late in all aspects of the game and we completely missed the first part of the game. The second half is a different story but it's really painful.
"It is not even about tactics, we just could not fight and we were late. It is difficult right now to assess the performances but there was a lack of pride."
Tottenham remain in fifth place with 53 points from 32 games but they are six behind third-placed Newcastle, who have a game in hand, and also six behind fourth-placed Manchester United, who have two games in hand.
With teams below them such as Liverpool and Brighton & Hove Albion also having games in hand, the question is not so much about the Champions League now for Spurs, but whether they will even hang on to a European spot.
"You can get punched once or twice but it was like we could not even react or bounce back," Lloris said.
"Newcastle deserve a lot of credit for starting the game at 100 miles per hour. They knew exactly what to do."
Tottenham resemble a club in disarray, having fired Antonio Conte (53) and replaced him with interim coach Cristian Stellini (48) and, on Friday, losing director of football Fabio Paratici (50) after his appeal against a two-and-a-half-year ban for false accounting was rejected by Italy's highest sports court.
They also face a fight to keep Harry Kane (29), their record scorer, at the club but Lloris said there were no excuses.
"We cannot hide ourselves behind the club's problems, we are professionals but today there was too much lacked," he said.
"There was a differences in level between Newcastle and Tottenham. We have two very difficult games to bounce back with."
Tottenham host Manchester United at home on Thursday and face Liverpool away next Sunday.
