The Irish province lost their first two fixtures in Pool 3 against defending champions Toulon and Leicester. It means victory over the Scarlets is a must if the 1999 European champions are to retain any realistic hope of getting out of the group.
And Williams, fresh from Wales’ Autumn victory over South Africa, is expecting Ulster to throw the kitchen sink at the Scarlets at Ravenhill on Saturday.
He said: “I think Ulster will be desperate. They never give up even though they are probably out of it now.
“They will want to give a massive performance, it is a tough place to go and we need the attitude we showed in Toulon in the first game where we were very competitive. Toulon outmuscled Ulster in the last round, and they lost to Munster in the Pro12 last week so they will want to try and take their anger out on us.”
There was nothing to separate the two sides when they met on the opening day of the PRO12 and played out a 32-32 draw at Parc Y Scarlets.
Williams captains the side from the centre, with Liam Williams coming back in at full-back. Samson Lee is back in the front-row after his breakthrough November campaign and he is backed up by returning lock Jake Ball.
The West Walians victory over Leicester in round two has kept them firmly in the mix for a quarter-final spot, and Williams knows how vital this upcoming double-header is.
“It is massive, this is like a semi-final this weekend. The boys have done well while some of us were away with Wales and got us into some form in the league,” he said.
“But we have to lift it as this will be at a different level. We did well in Toulon and beat Leicester and we know a result this weekend would put us right in there.”