Spurs took an early lead through a Cristian Romero header on 11 minutes but failed to capitalise further on their first-half dominance, with West Ham netting a pair of counter-attacking goals in the second half through Jarrod Bowen and James Ward-Prowse.
"We lost the game which is unacceptable," Son told Amazon Prime in a postmatch interview. "You get the lead five times in a row and losing the game I think is unacceptable and as players we should take responsibility.
"West Ham have always been tough to play against but look we were soft. Especially in the Premier League, even if you are winning 2-0, 3-0, you don't know what will happen in the end."
When asked if the side's failure to put teams away was psychological, Son said: "Not at all. But as I said before the players should take responsibility, and the fans don't deserve this. When you go 1-0 up early you should bring even more energy. We didn't and that's why we lost."
The result marked the first time since 2008 that Spurs have suffered three straight home defeats.
Manager Ange Postecoglou said his side must start grinding out results and made clear his team are more focused on winning than playing an entertaining style of football.
"It's another game where we dominated a game of football and we didn't turn that into something more... we have a long way to go as a team," Postecoglou told a postmatch news conference.
"Us being good means us being 3-0 up. This is not about playing good football, this is about winning games of football.
"I've said that from the start, that all I wish to set up teams to win games. Being 1-0 up at half-time was not a good performance by us. We should have been three, four nil up in the first half."
"I think at the moment we're going through this spell where we're so-called playing good football but I don't see that," he added. "What I see is us not showing any real clear conviction in what we're doing."
Injury-hit Spurs were without nine first-team players for Thursday's contest, including defender Micky van de Ven and playmaker James Maddison.
The result means Tottenham remain fifth in the Premier League on 27 points after 15 games, a marked difference since the end of October when Postecoglou's side were five points clear at the top of the Premier League.
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