A much-changed Spurs side found themselves 2-0 down at half-time to a Paul Hayes brace before Son Heung-min and Vincent Janssen levelled matters midway through the second half.
Garry Thompson's header had Wycombe dreaming again with six minutes to go, but Dele Alli equalised before Son struck the decisive blow in the seventh minute of stoppage time.
"That is the FA Cup. Every time we play in it, anything can happen," Pochettino told BBC Sport.
"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.
"We did not underestimate them. Credit them, we cannot play them down. It was very difficult for us.
"It was difficult to stop them, they showed more desire and quality on the pitch. It is only fair to say the truth.
"This is the beauty of the FA Cup. It's magic. This is completely different to Spain or France. It is the oldest competition in the world and the teams and people try to win to lift the trophy. It is always special.
"We will try to win the three competitions. It is tough because you need all the squad."