It was cruel on the visitors who will feel that they deserved at least a replay, and Pochettino was quick to pay credit to them after the game.
The 44-year-old is quoted by BBC Sport as saying: "That is the FA Cup. Every time we play in it, anything can happen.
"Wycombe played very, very well in the first half. In the second half we increased our level and pushed a bit and I think we played better than them but in football you need some luck and with the last chance we scored and won.
"Full credit to Wycombe they played very well. Congratulations to them because they were heroes."
Spurs are attempting to reach the final of the competition for the first time since 1991.