Cook insisted it was a compliment to both clubs to have the national manager in attendance.
Asked whether he knew Southgate had been present, the 21-year-old told the Daily Echo: “I wasn't aware. I don't know if he was watching me but, if he was, I guess it's good.
“I will just keep getting my head down and concentrating on football and that's the main thing, to keep enjoying it and improving.
“If he came to watch these teams, it's a compliment to us all."