Rovers were unable to repeat their Carabao Cup antics of last season as Blackpool came from behind to claim a second-round victory.
Alfie May put Rovers in front midway through the first half, but goals from Michael Nottingham and Harry Pritchard saw the Seasiders progress through to the third round of the cup.
The visitors started the brighter, with Nottingham heading just wide from a Chris Taylor corner just 10 minutes in.
Paul Taylor, making his first start in a Rovers shirt, had two great chances to open the scoring himself, with May working hard down the right-hand side to square to his fellow forward.
Taylor's first attempt was saved superbly at point-blank range by Mark Howard, before turning his second effort just wide of the post.
The Rovers duo would combine once again five minutes later, and this time, they would get their reward for a brilliant piece of play down the left.
Taylor received the ball from a Danny Andrew throw-in, twisting his defender before putting the ball forward for May.
May got to the ball ahead of Ben Heneghan, turning his defender and unleashing a powerful left-footed drive into the top left-hand corner, clipping the underside of the bar and rippling the back of the net, leaving Howard with no chance.
The Seasiders drew level 15 minutes later. A Blackpool corner came into the area, with Heneghan knocking the ball down into the ground, with Nottingham flicking on into the top corner.
A slow start to the second period for both sides saw limited chances at either end, and with the next real chance, the deadlock would be broken once more, this time with the Seasiders going in front.
A throw-in from the right by Nottingham was launched long into the area, with Pritchard able to stick a leg out to it, and his poor connection somehow squeezed its way into the near corner, putting Blackpool in front for the first time on the night.
Ben Whiteman, fresh from his goalkeeping exploits at the weekend would be first to try and get Rovers back on level terms, testing Howard from distance, only to see his shot sail into the hands of the Seasiders stopper.
Armand Gnanduillet would have one last attempt to extend the Seasiders' advantage as the clock ticked on, countering on a Rovers attack down the other end, only to see Ian Lawlor tip the ball over the top and behind.
Despite late pressure from the hosts, Rovers were unable to draw level once again, and it would be the Seasiders who would progress through to the next stage of the Carabao Cup.
Rovers return to Sky Bet League One action this Saturday when they travel to early league leaders – and manager Grant McCann's former club – Peterborough United at the ABAX Stadium.