The Gunners fullback was impressive in World Cup qualifying victories over Albania and Latvia.
Parlour told Tribalfootball.com yesterday: "He looked so composed on the ball and didn’t look nervous at all. I know he is a confident lad and to go out and perform like he did is testament to him. He got a lot of the ball in England’s build up play and to score on your debut is stuff of dreams.
"I saw he said he was lost for words post match and this says it all. He knows this is the start and he must continue to perform day in day out in training and perform on the pitch for Arsenal. He has such a bright future and a good family around him as well. I wasn’t surprised as he has such a good temperament about him.
"In terms of left backs he is one of them for sure. He is still so young and plenty more with experience, so he must keep his feet on the ground and has a big future."
On England's start under new coach Thomas Tuchel, Parlour felt it was a job well done for his opening two games.
Parlour also said: "I was at Wembley last night and England did what they had to go and win the game first and foremost. When teams defend so deep and only interested in keeping the score down then you have to be creative and patient. I have played in games like that for Arsenal over the years.
"You go so close to scoring and then need to work another opportunity and keep going. So England did what they had to do. It’s good for players like (Jarrod) Bowen and (Morgan) Rogers to get game time.
"But England will have tougher games to come, so it’s important for the squad to get used to Tuchel and his training and demands and vice versa for Tuchel to understand what players he wants to play and see how they work."
- Ray Parlour was speaking Tribalfootball.com on behalf of NetBet Online Casino