The home side started the game brightly, and took the lead through Son in the 40th minute.
However, Tottenham could not maintain control over the game, and surrendered possession and initiative to United in the second period.
Son told the club's official website: "It's a really sad afternoon. I'm really not bothered about the goal.
"I really wanted to win, especially after the last game [at Newcastle] when I came on, back from injury, we were leading and drew.
"I don't know what to say – I'm really sorry about it and feel bad. I know those supporting us are really disappointed – I think they are more disappointed than us so I feel really bad and really sorry about it. I really, really wanted to win – I really do."