The 29-year-old made himself unavailable for England selection two years ago, stating that he wanted to focus on his club career.
Clarke told reporters: "If you're looking at a top-line goalkeeper, every mistake is analysed. If you go with England, it's magnified 10 times.
"Ben decided he'd rather spend time with his family than be put under that stress and strain and we respect that. For us as a club, it's good."
Foster made five appearances for the Three Lions in his three-year international career.