The Czech shocked the world number one to emerge victorious in four sets at Flushing Meadows and the 26-year-old failed to hold back his excitement.
"It couldn't be better," Berdych said. "There's no better moment so far than this one."
The sixth seed faces Andy Murray on Saturday for a place in the final and admits that he may have to improve if he is to defeat the Olympic champion.
"I'll just try to bring something from today and try to add something a little more for my next match," he added.
Berdych has moved past the quarter-finals of a Grand Slam only once previously, at Wimbledon in 2010.