The Eagles have now won five successive games to move to the top of the NFC East and are closing in on a place in the NFC playoffs following their comeback victory over the Detroit Lions last week.
Williams told the Philadelphia Inquirer: "We understood the season wasn't over just because we were 3-5.
"Everyone understood it's a long season and it was going to take a while for us to get acclimated to each other.
"I'm confident that if we happen to stumble, God forbid, that we'll get back in it. This team doesn't quit. I don't see a letdown with this team if we do happen to falter."
Chip Kelly's side are 8-5 in their season going into their week 15 clash with the Minnesota Vikings on Sunday.