"I know I haven't played to my potential, which is frustrating," said Williams.
"I don't blame people for doubting me because I know I haven't been playing as well as I could.
"But I've known I was good enough from the start, it was just about getting that performance.
"This was a massive game for me - I knew eyes were on me and that there were a lot of doubters out there.
"I also knew it was my last game for the Lions, so I had to go out and perform.
"I just went out there, didn't force anything, got as involved as I could and played particularly well.
"I didn't go out to dazzle, it was all about working players outside me. When I got my hands on the ball I could see the Boks were looking at me to do something. But when I offloaded it meant just as much to me."
Even though he has only played a bit-part in a series the Lions lost 2-1, Williams said the tour would go down as one of the highlights of his career.
"From day one it's been special," he said. "We've been a tight-knit family, worked hard on and off the field and made some great friends.
We knew it was the last time we would play with this squad, this bunch of guys, and you don't need more motivation than that
"There are no egos, no worries about people being bigger than others.
"It was disappointing to lose the series, because we felt we deserved something out of it, but the game was incredible and I was really proud to be part of it."
Number eight Jamie Heaslip, who pushed Williams hard for the man-of-the-match award after an outstanding individual performance, praised the Lions coaches for their part in the victory.
Head coach Ian McGeechan took the players on a safari after their heart-breaking defeat in the second Test last Saturday - a decision Heaslip describes as "a blinder".
"They allowed us to let off a bit of steam and when we came back in on Wednesday we were ready to go," said the Irishman.
"The last word from them before the game was a warning that all the good work of the last six weeks would be undone if we didn't play to our potential.
"We knew it was the last time we would play with this squad, this bunch of guys, and you don't need more motivation than that."
The Lions fly back to London's Heathrow Airport on Monday.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.