After their string of giant-killing acts, Rovers were dumped out of the competition by a Notts County side which plys its trade in League Two.
Substitute Myles Weston scored the only goal of the game, drilling his angled left-foot shot past keeper Neil Sullivan at the start of the second period of extra time.
Rovers huffed and puffed but they rarely looked like getting back on level terms in the last 14 minutes.
They began with a handful of changes to the side that beat Derby County in Saturday's Championship opener at Pride Park.
Defenders Jos van Nieuwstadt and James Chambers and midfielder John Spicer all made their starting debut for the club.
Rovers were the first to threaten, midfielder Mark Wilson testing keeper Kevin Pilkington with a well-struck 25-yarder in the fifth minute.
Wilsonb did well to tip the ball over the bar for a corner.
Rovers went close to breaking the deadlock on 22 minutes when skipper for the night Gareth Roberts beat Pilkington from a direct free-kick from just outside the area, but the ball clipped the top of the bar.
The quality of the strike underlined what a threat the former Welsh international defender is now becoming from set-pieces, whether shooting or supplying a cross.
County went close to taking the lead on 34 minutes from Neil MacKenzie's 25-yard free kick, which keeper Neil Sullivan tipped over for a corner.
Chambers, who had pushed on deep into the County half, picked out Heffernan in the box but the striker headed wide.
Heffernan did better with a shot from just inside the area a minute later, firing narrowly wide of the near post.
Sullivan failed to make a clean catch when the ball was pumped into the box from the left, but he redeemed himself by scrambling back to pluck Jay Smith's 25-yarder out of the air.
Wilson wasn't far off target with a 25-yarder in stoppage time.
Rovers striker Lewis Guy just cleared the crossbar with a 50th minute header after getting on the end of a cross by Richie Wellens.
Pilkington got down well to smother Spicer's low shot on 56 minutes after the former Burnley man had gone past defender Paul Mayo just outside the area.
Rovers brought on Stuart Elliott, who had looked one of their most dangerous attacking players in pre-season, in place of James Hayter.
Heffernan was high and wide with a 25-yard volley three minutes later.
It needed a superb tackle by Roberts on 66 minutes to deny Ben Fairclough a shooting chance on the edge of the six-yard box in front of goal.
It was all County at this stage and Smith tested Sullivan with a shot from the left.
He then picked out striker Delroy Facey with a pin-point cross, but Facey headed over from ten yards out.
With County still looking the side most likely to open the scoring, Rovers boss Sean O'Driscoll made a double substitution on 77 minutes.
James Coppinger and Martin Woods replaced Wellens and Spicer.
It didn't take Coppinger long to make his mark with a trademark jinking run, while Woods shot just wide from 30 yards.
County skipper Mike Edwards shot over when he was well-placed after the ball had been pumped into the box after a 22-yard free-kick had been blocked by the wall.
Guy also had a late chance to win the game in stoppage time but he shot weakly at Pilkington.
It was to prove a costly miss.
CLICK ON THE GREEN PLAY BUTTON ABOVE TO SEE PICTURES FROM THE MATCHWhat do you think? Post your comments below. Roller-coaster start for Rovers: Read it in the Green 'Un - out Saturday READ MORE Football headlinesMore BladesMore OwlsMore SpireitesMore RoversMore RedsMore MillersMore Ice HockeyMore rugby leagueMore rugby unionMore boxingSports columnistsAll sport categoriesThe full article contains 699 words and appears in Sheffield Star newspaper.
