Williams said: "The 20 minute period in the first half when we went 22 points behind was a killer. You just can't give teams like Fiji that sort of lead.
"We're devastated and it's hard to put into words how I feel; we've only got ourselves to blame.
"We tried our best to claw it back but we kept turning the ball over. We allowed Fiji to get back into the game and it was too much for us.
"It will be a tough few days when we return home but we gave our best but it wasn't good enough.
"There's a lot of young players in the squad and they'll learn a hell of a lot from today. We've shown glimpses in matches that we're a good team and we know the talent is definitely there."
But Fiji have some talent of their own and the performance was one that saw them progress to the final eight of rugby's World Cup for the first time since 1987.