Williams' first goal for the club rescued a late point at Stockport County - and they will now look to build and that and pick up their first win in 12 games as they welcome second placed Northampton Town this evening.
And the experienced forward, who paid tribute to the 1,250 travelling fans who made the trip to the North West on Saturday, believes they can be a real help to the players as they look to address their tough run.
He said: "We are working hard every day and this group is way better than where we are.
"But words are cheap and we have to start getting results.
"The support has been incredible and hopefully they do the same again on Tuesday because having them behind us is a real weapon.
"And hopefully we can give them something to cheer about.
"Football can change so quick, it is not nice being on these runs and sometimes maybe fans have the wrong perception of players that they turn up and just go home.
"But it effects our whole week, my wife knows when I've lost in training let along games, we want to win all the time and it does hurt us, and it is painful, but we have the belief that it will change."
Northampton head to the Bescot just two points behind leaders Leyton Orient after a superb start to the campaign.
And Williams believes Walsall's squad has the potential to do the same - and compete at the top end of the division.
"That is where we want to aim to be," said Williams.
"In football, when you get on a run and get momentum we could chase and get up there.
"We have a bit to do but it has to start somewhere, and hopefully this is where it starts."