Spurs surrendered a two-goal lead on their way to being beaten 4-3 at home on Sunday afternoon.
Despite Son's late goal, Ange Postecoglou's side were unable to salvage a point as their poor form continued.
The defeat means Spurs have now won just one of their last seven Premier League matches.
As a result, they have slipped to 11th in the table and are seven points adrift of the top four.
Speaking after the match, Son gave an emotional interview as he called for togetherness from all those associated with the club.
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The Spurs captain told Sky Sports: "It's very disappointing. I don't know what to say at the moment.
"We conceded very sloppy goals. It feels like we lost because of these small details. On such a big stage, you need to step up and score in these moments.
"I feel like I let the team down and I feel very sorry for the team."
He continued: "We can't concede goals like this. We can't dive into this situation. I can stay here all day talking about the mistakes but I'd rather blame me with the chance and I'd rather take the blame.
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"I had a bit of a different thinking when I was running to the ball. I'm also human and I miss. I feel the pain because it's such an important moment of the game. The team tried.
"We got to stick together in such difficult moments, it's very important and it's why we need big support.
"The players are very young and they need support more than before and more than we had. The fans were always supporting amazingly but I think it's time the players also need to step up.
"We need some big support and big cheering up."
Son had scored his third league goal of the season to provide some late hope after four unanswered goals from the visitors.
However, the Blues held on to close the gap to leaders Liverpool to four points.
Spurs will be hoping for a response away to Scottish giants Rangers in the Europa League on Thursday night.
Meanwhile, their next league match is a trip to Southampton on Sunday.
Son's call for support at home will have to wait over a week, though, with Spurs hosting Manchester United in the Carabao Cup on December 19.
They also face home league matches against Liverpool and Wolves either side of a trip to Nottingham Forest before the end of the year.