A poor opening period saw Rovers trail by three goals before Jordan Preston added to his growing reputation by heading home a Liam Langford centre on 40 minutes.
However City added two further goals either side of the break to take a commanding 5-1 lead.
Rovers rallied in the latter stages, making it 5-2 on 80 as Preston followed in after Dean Rittenberg had seen his shot saved.
Preston then missed a great chance to reduce the scoreline further, but completed his hat-trick in the final minute, taking advantage of a City error at the back as the game an entertaining 5-3.
"From our positive point of view the boys kept going and kept the scoreline to a respectable level," said coach David Lowe.
"We were struggling at 5-1 down but managed to get a foothold in the game through Jordan Preston.
"We ran out of time in the end but Man City were the better team for longer periods.
"I'm delighted for Preston with his hat-trick, his general play was good as well."
ROVERS: Raya, Vicars, Butterwick, Bauress, Langford (sub Cham 70 mins), Harris (sub Tanner 85 mins), Wassi, Torres (sub Joel 80 mins), Doyle, Rittenberg, Preston.
Subs not used: Lavelle, Wall.