"There has been a bit of soul searching, we have spoken about it, we have all looked at ourselves in the mirror and asked what we could do different and better," Williams told British media.
"We've been really trying to get back on it, not accepting things and raising the standards of our play and stuff.
"Hopefully now this gives us confidence. We have just beaten Arsenal and now got one of the biggest games of the season, if not the biggest coming up, and hopefully we can build on it."
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Manager Ronald Koeman said before Tuesday's victory that his team had shown themselves to be "weak" and Williams felt the players had delivered the perfect riposte.
"I like to think we answered those questions but now we have to build on it and make sure it's not just one game," Williams added.
"The fight was there with a bit of quality too. It's an Arsenal team which has been unbelievable this season and if we can perform like that against them, we should be able to do it every week."
(Reporting by Shravanth Vijayakumar in Bengaluru)
