Pochettino believes Shaw has shown Roy Hodgson that he has the quality to deliver in international football.
He said: "I think Roy Hodgson has a very big problem on his hands.
"I don't know what is going through Roy's mind at the moment regarding Luke Shaw but in light of the 45 minutes he played he showed he deserves to be in the team and has the quality to be in the team."
Pochettino felt that Shaw's performance was a great moment for the club, as well as the player and his family.
"I thought it was an amazing moment for him, for Southampton Football Club in general and especially all the managers and directors he's had in the academy," he said.
"To see a child from ten-years-old to making his international debut has to be a moment of great satisfaction and of great pride."
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