Townsend catapulted himself to stardom this month with stunning performances in England's climactic World Cup qualifiers against Montenegro and Poland.
Dawson said: "He has not changed, he is still the same player he was two weeks ago.
"He has just been in the media spotlight and he has taken it well.
"It was a top performance. He was man of the match and scored a goal. He is playing well and is full of confidence.
"He's carried on where he left off for England."
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