Rovers bowed out of the play-offs in cruel fashion after following victory at The Valley with a penalty shootout defeat.
Rovers were left with it all to do after Krystian Bielik headed home in the second minute to give the home side a 3-1 advantage on aggregate, but Rovers did not know when they were beaten in an enthralling game.
Captain Tommy Rowe quickly drew Rovers level on the night with a stunning long-range effort, reducing the deficit in the tie back to one goal.
Both sides pushed for goal in an enthralling tie played in competitive but fair spirits, with Andy Butler heading in after 88 minutes to level the tie and secure extra-time.
The extra 30 minutes were played in the same intense spirit as the first 90 on the night, and John Marquis put Rovers ahead in the tie for the first time 10 minutes in.
That aggregate lead did not last, though, with substitute Darren Pratley netting for the hosts to secure a penalty shootout.
Although Rovers keeper Marko Marosi pulled off a save from Naby Sarr, the home side went through after Marquis and Rowe were unable to convert their spot-kicks.