The 16-year-old became the seventh youngest player ever to appear in the Premier League, and Quinn believes he is a star of the future.
"They were excellent and the young lad, young Reece Oxford in the middle of the field – well that's dream stuff, to say a star is born it's absolutely true," he told Sky Sports.
"The kid's not only broken some phenomenal records and played the game, he was outstanding.
"I kept a real close eye on him, sometimes off the ball he'd turn around and give out instructions, pointing fingers, letting things develop.
"He had a maturity today which was so hard to understand because you think he's going to be lost out there and that all the others players are going to have to rally round him and it was the exact opposite."
Oxford started at the base of the midfield for the Hammers and held his own against the likes of Mesut Ozil and Aaron Ramsey, indicating to Quinn that those close to him can be extremely proud of him.
"He's got a great build, his physique is good and his mobility is very good, he handled the ball really well, he knew when to drop back and make a fifth defender," Quinn added.
"He was a perfect player for his manager today and to do that at 16 years of age is just incredible. I'm really pleased for the lad and I'm sure all his mentors all the way up, and his family as well, they're pinching themselves as well.
"They can be very proud of him and we'll be hearing about him for a long time to come."