The Baggies have not recorded a Premier League win since August, when they won their first two games of the campaign.
Since then, they have plummeted down the table and sacked former boss Tony Pulis.
While Gary Megson took charge on an interim basis, Alan Pardew is now at the helm and West Brom sit 17th after 15 games.
West Brom have drawn their last three games in the league and Livermore is adamant the squad has the quality needed to push on.
He told the club's official website: "The lads want to do well for each other, for the fans, for our own families, for the backroom staff - we want to do well for everyone.
"The new manager has come in and he’s been fantastic. He has shown the positivity he wants us to show - he’s shown the belief that he’s got in us to go forward.
"It’s not panic stations just yet! We have some great players in the dressing room and some great staff as well.
"We’ve definitely got enough to get ourselves up the league."