Widespread fan unrest has hung over the KC Stadium upon their return to the Premier League over owner Assem Allam's plans to change the club's name.
Four defeats from their last five league games have done little to placate the support, and Sunday's visit of Brendan Rodgers' side may worry many.
Only Manchester City have scored more than Liverpool this season, and Bruce hopes the home fans will get behind the players, rather than focus their ire on the club's hierarchy.
"Since I've walked through the door the supporters have been nothing but fantastic towards how the team tries to play," he said.
"I know there's some issues about badges and names, but it's Liverpool at home, a game we've been waiting for.
"Let's enjoy the occasion and the supporters can play their part. When they're behind the team, it gives us a helping hand.
"It's going to be difficult, but we need them to play their part and forget about banners for now, and let's make sure we get points. I'm sure they're all with me on that as well."
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