The Aviva Premiership side beat Stade Francais 29-6 in Paris yesterday evening to progress to the last four.
The director of rugby told Sky Sports News: "This is the end of the season and it's when things are won and lost so we're delighted with this win.
"It was a hugely satisfying performance. It was an incredibly physical game and intense as expected.
"We know they [Stade] had players missing but they also had plenty of good players on the pitch and coming to France is always hard, especially here."
Quins will face Northampton Saints for a place in the final later this month.