The 28-year-old booked his place in the last four at Flushing Meadows - surpassing his previous best performance in a Grand Slam tournament - with a 6-4 6-3 6-2 win on Arthur Ashe.
"Normally I can be a little bit nervous and I can lose a few games because of that, but today I was just focused on my game," Reuters quotes him as saying.
"It's amazing for me to be in my first semi-final of a US [Open], especially after beating Andy Murray, the defending champion. He won Wimbledon, too. To beat him in three sets, the way I was playing today, is quite good for me.
"It's my moment and I'm enjoying it a lot. I'm really thankful for [Federer] because he has helped me a lot. But today, for sure it's my moment. Roger texted me straight after the match. He told me congrats."
Wawrinka will play either Novak Djokovic or Mikhail Youzhny in the semi-finals in New York.