The Scotsman, who won a gold medal at the London Olympic Games this summer by defeating Roger Federer at Wimbledon, progressed into the next round after overcomingAlex Bogomolov Jr in four sets.
"He gave himself a six or seven out of 10. That's about right," BBC Sport quotes Castle as saying.
"There are six matches for him to win his first Grand Slam. This was just about him clearing the hurdle. It's going to be no surprise to see him sailing into the second week. I don't think I've ever seen him playing better than in the last two or three months."
The 25-year-old will face Ivan Dodig in the next round.