The 23-year old winger was a key figure in the US' CONCACAF Gold Cup triumph, scoring two winning goals in the tournament, including the only goal in the 1-0 victory over Panama in Sunday's final.
Shea will soon head back to England and Klinsmann wants him to put his best foot forward as he goes about impressing new Stoke boss Mark Hughes.
"I think that element with Brek, coming in and taking people on and having a surprising element in his game, I think every opponent would feel that," Klinsmann said.
"As a coach, you think, if you do something now, what would an opponent feel from your end. And you see a guy like Brek, [he's] unpredictable, for himself and for the opponent."
He added: "He knows that he has a way to go, he knows that he has to fight for his spot at Stoke, which he will do from tomorrow on. But he has this hunger and he has this willingness to learn."