Writing in his newly released book, the 28-year-old says the forward's "utter contempt" for fellow footballers angered him and added that he has "no time" for the Uruguayan
The Swans, led by now-Reds boss Brendan Rodgers, earned a creditable 0-0 draw against Kenny Dalglish's men, frustrating the hosts by keeping possession impressively.
But, writing in his new book, My Premier League Diary, the 28-year-old admitted he almost lost his cool with the Uruguay international.
"He dived more than any other player I've played against before – it was so bad I was genuinely shocked," he wrote.
"Throughout the game, he just dived down and screamed at any given moment.
"Suarez has that aura about him that says, 'I'm untouchable', and his manner and behaviour made me want to knock him out.
"I'd go as far as to say that the manner in which he approached the game, with utter contempt for us all, means that he's streets ahead of any player I've truly disliked since I've been in the Premier League."
The defender further underlines his dislike for the former Ajax forward when recalling the reverse fixture, a 1-0 victory for the Welsh club.
"They won a corner, and I appealed to the ref to say that it had come off him last. He said something to me with a bit of a snarl, so I just told him to shut his mouth," Williams adds.
"Now, obviously, diving has crept into the game more and more in recent years and, as a defender, you have to be aware of it.
"But even the players you know that like a dive at least wait until there is some sort of challenge or contact. Not Suarez.
"A couple of times I'd hear the scream, see him writhing on the floor and for the life of me couldn't see where the contact could have been.
"Even [referee] Phil Dowd had enough of him and said: ‘You’re doing too much, Luis’ at one point.
"The sad thing is that he’s a brilliant player and I rate him very highly, but he just possesses this temperament that I can’t stand to see in a fellow footballer.
"Having played against him twice now I just have to say that I don't like the bloke. Basically I have no time for the guy at all."
Swansea host Liverpool at the Liberty Stadium on Sunday afternoon.