The squad were put through their paces by manager Garry Monk on Monday in Chicago with a triple session at the University of Illinois.
"It was a very tough session to start with, but we realise that as much as it does hurt right now it is helping us all in the long run," Williams told the club's official website.
"We will be very fit this season if pre-season training is anything to go by. We had a triple session to start, and it will be very hard for the next few days at least, but no pain no gain."
Williams, who signed a new four-year contract on Friday, will line up alongside his teammates against Manchester United for the opening day of the 2014-15 season on August 16.