Sky Bet League Two Wycombe, who are 70 places below Tottenham in English football's hierarchy, led this most pulsating of FA Cup ties on two occasions before Dele Alli equalised in the 89th minute, and Son sealed the win in the seventh minute of added time.
Garry Thompson then appeared to have sealed a shock win when he scored Wycombe's third with only six minutes left.
"In that moment, I said it would be tough to score again," Pochettino said.
"You always believe and try to win and be a little bit lucky, and today we got a little bit lucky to get into the next round.
"That is football, and I am sure they are very sad now and disappointed, but we can do nothing. Today was for us, and maybe on another day it goes for them."