Chambers, 19, was one of four teenagers who lined up for the Saints in Tuesday's 2-2 draw with Arsenal.
He said: "Any group of people like us coming through are aiming to do what those United players did.
"We are doing everything we can to try and achieve that.
"When I was young I used to play right wing and I used to look up to David Beckham and other members of that team like Gary Neville.
"I dreamt of playing in the Premier League like they did.
"I just try and go into it thinking this is my chance. The more games you play the more confident you get.
"The manager has been really good with all the young players. He gave me my debut and I cannot thank him enough.
"The club and the manager have got a lot faith in all the young players."
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