Richard Stearman and Andreas Weimann got the goals for the visitors, with a reply from Divock Origi unable to shake the Reds from their 2017 struggles
Liverpool's disastrous start to 2017 continued as Wolves won 2-1 at Anfield on Saturday to dump the Reds out of the FA Cup.
Richard Stearman opened the scoring early on with a header from close range, before Andreas Weimann made it two shortly before the break, with Divock Origi's goal coming too late for the hosts to try and snatch a draw.
Jurgen Klopp's men had won just one of their seven games since the turn of the year ahead of this encounter, losing further ground on Chelsea in the race for the Premier League title, as well as being eliminated from the EFL Cup.