The Baggies clinched a nervy victory over Sheffield United at The Hawthorns last weekend, which moved them out of the drop zone.
Fulham’s surprise 2-1 triumph at Leicester on Monday night, though, means they are now back in, and Bilic has stressed the importance of building momentum after breaking their duck.
“That is what I told the boys. We were allowed to be proud and enjoy the Sheffield United win,” he said.
“But now we are asking even more because we have shown we can do it. It’s not hopeless, we can do it.
“It hasn’t been hopeless, look at the last few games against those big guns.
“We showed what we can do but we didn’t get any rewards.
“But we kept a good atmosphere and good work ethic and good energy in the group.
“This wins should make it go up again, so we are going to be more demanding.
“We don’t want to lose this opportunity to hopefully keep this momentum going.”
Conor Gallagher got the goal – the Chelsea loanee’s first in the top flight – against the Blades, with Albion surviving a late onslaught to clinch the much-needed three points.
Chris Wilder’s side missed some big chances – most notably Lys Mousset firing over from point-blank range at the death – but Bilic insists his men were due some luck after a solid performance against current table-toppers Tottenham and VAR controversy at Manchester United.
“We definitely deserved it. We have had some good performances, we have trained well, our shape has been good, everything,” he said.
“But you need the reward and Sheffield United was that.
“I told myself, my staff and the boys what we are going to need to stay up. One of those things is a bit of fortune.”
Bilic also insists goalkeeper Sam Johnstone has a key role to play moving forward, having impressed with top-drawer displays between the sticks as of late – making a series of super saves in the success over Sheffield United.
He added: “One of those things is a quality goalkeeper – and we are going to need Sam in every game.
“We are not a team that is going to block our goal and not let the opposition come close to it.
“Nobody can do that, especially now with the games so stretched because there are no fans.
“Sam, at the moment, is doing brilliantly for us, but the team needs that.”
Meanwhile, Bilic is hoping Conor Townsend’s knee injury picked up against the Blades does not keep him out of the Palace game
The defender, another who has been in fine form, was forced off in the 75th minute with what is thought to have been an impact injury rather than a twist and is being assessed this week.