Murray defeated the world number one 6-2 6-1 6-4 on the All England Club's Centre Court on Sunday to become the first British male to win the event since 1908.
"I didn't expect that. I felt so fresh on the court today. I didn't fell nervous at all," he told BBC Sport.
"I've had a lot of tough losses in my career but this was the best way to come back from the Wimbledon final.
"The momentum that [Team GB] has had in the last couple of days has been so good."
The medal is Britain's first in the tennis since 1996, when Tim Henman and Neil Broad claimed the silver medal in the men's doubles at the Atlanta Games.