The highly rated full-back signed from Championship outfit Leeds United during the week and was a late call-up to the bench for the game against title challengers City.
An injury to Carl Jenkinson forced manager Slaven Bilic's hand to give the 22-year-old his top-flight debut earlier than expected.
"It was unbelievable," he told Sky Sports. "To come on in 13th minute wasn't something I was expecting, but I've dreamt about this moment since I was a little boy and to be able to come on and make my Premier League debut, I'm unbelievably pleased."
Byram said just making the bench was a surprise.
"One of the lads had a bit of a knock in training. That meant he wasn't involved and I got the call up onto the bench," he said.
"I was just pleased to be involved and to be able to come in and see how everything works on a match day.
"I wasn't expecting to come on as soon as I did, but I enjoyed it."
So far, coming up against team-mate Dimitri Payet has proven the the most eye-opening part of life at Upton Park.
"Training has been tough, [Payet is] hands down the best player I've had the chance to play with," Byram added.
"If I can learn a thing or two off him I'll be a better player."