Son and his Spurs teammates came from 0-3 down at halftime to eventually lose 2-3 on Sunday.
The captain later said: "We could have come back.
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"I feel that we had a good chance and good opportunities.
"They were clinical and strong in the air. We had plenty of chances, we hit the post and had a goal disallowed."
Tottenham conceded two goals from set pieces, and it was especially those that troubled the South Korean star after the game.
"As I said before, this is a big game and we had to be strong on set pieces.
"Arsenal are of course good, but I think everyone needs to pick themselves up. Now we are working on the set pieces, staying strong and clawing at it."