Scoring goals hasn't been a problem for Rovers this season, but keeping them out at the other end has as Liverpool ran out 4-2 winners.
The home side opened the scoring through Welsh international Harry Wilson before Rovers levelled moments into the second half.
A short corner saw Jordan Anderson's cross parried by the Liverpool goalkeeper and Jordan Preston was on hand to stab the ball home.
But three goals in quick succession saw the Reds run away with the match, Alex O'Hanlon, Daniel Trickett-Smith and a second goal for Wilson putting Liverpool 4-1 in front.
It could have been worse but for a penalty save from Rovers debutant Ben Killip.
There was time for a consolation as Jordan Preston grabbed his second of the game in the final moments to take his goal tally for the season to 11.
"To be fair for long periods in the first half we were second best," said coach David Lowe. "We didn't believe in ourselves.
"We rallied slightly at the beginning of the second half when we equalised and missed a couple of chances to get a foothold in the game. But three quick goals in succession gave us to mountain to climb.
"It is a tough environment against fantastic opposition every week, hopefully they'll learn and benefit in the long run."
ROVERS: Killip, Anderson, Scott, Lavelle, Doyle (sub Butterwick 46 mins), Harris, Vicars, Wassi, Torres (sub Cham 60 mins), Joel (sub Tanner 79 mins), Preston.
Subs not used: Williams, Pierce.