Tottenham went to St James' Park on Sunday knowing a point would likely be good enough to see them clinch second place in the Premier League and finish above Arsenal for the first time since Arsene Wenger took the helm at their north London rivals.
But instead Spurs were hammered by Newcastle, who went 2-0 to the good thanks to goals from Georginio Wijnaldum and Aleksandar Mitrovic.
Mitrovic was shown red for a dreadful high challenge on Kyle Walker after Erik Lamela pulled one back for Tottenham, but Moussa Sissoko's penalty and late goals from Rolando Aarons and Daryl Janmaat gave Newcastle a comprehensive triumph.
Arsenal's 4-0 win over Aston Villa meant Tottenham finish third, with Pochettino telling Sky Sports: "First of all I want to apologise to our fans, our supporters because it was a shame what happened on the pitch.
"I apologise to our families that suffered behind us. It is difficult to arrive home and explain what happened here. I'm very disappointed, I think it was my worst game as a manager.
"We need to learn, we need to improve our mentality. It wasn't a tactical problem it was a mental problem. When you go into the pitch you need to give 100 per cent. We need to show more character. "
Pochettino conceded it has been difficult to help the players maintain a positive mentality after seeing their title hopes end with a 2-2 draw at Chelsea this month.
He added: "It's my responsibility, I'm disappointed but it's good information for decisions in the summer.
"This was our challenge to keep the mentality and I think [after] Chelsea we showed a lot of mental weakness against Southampton [a 2-1 defeat last weekend] and today [Sunday]."