The Denmark global produced an excellent display at the Liberty Stadium on Saturday, breaking the deadlock early on and then completing the scoring in the second half after Erik Lamela had struck.
"It was a very good performance", Pochettino told the BBC. Lamela, playing behind Son Heung-min, who was given the nod up front ahead of Fernando Llorente, also enjoyed himself as Spurs made the most of the space afforded to them by a severely depleted Swansea side.
Eight-times FA Cup winners Tottenham are looking to lift the trophy for the first time since 1991, since when they have lost seven semi-finals, most recently to Chelsea previous year. The competition may not be what it once was, but it would be a major step forward for the club if they were to lift the trophy in May. Renato Sanches could potentially be back in the match-day squad after injury, but Wilfried Bony, Leroy Fer and Angel Rangel will all miss out.
Pochettino was pleased with the way Tottenham took control without Kane and Dele Alli, who was only a late substitute.
Any chance of a Swansea comeback was long gone as the match entered its final stages, allowing Spurs to ease to successive FA Cup semi-final appearances for the first time since 1981-82, when they won the competition.
The South Korean global has emerged as a prominent player under Carlos Carvalhal and he will be important this weekend.
"We played against a strong side - I said before the game it was David against Goliath, we know the difference between the teams". With survival in the Premier League being the club's main objective, we could see the Welsh outfit make changes from the side that took the field against Huddersfield last weekend.
Christian Eriksen gave Spurs the lead early on after he finished a good run with an exquisite finish.
Swansea never got going on a freezing afternoon in south Wales and can now concentrate on trying to preserve their Premier League status.
"With the Premier League or La Liga, the Bundesliga or Serie A, you need to deserve to win this type of title".