Devante Cole's goal on the stroke of half-time proved to be the difference between the two sides in a lively encounter at the Highbury Stadium.
Damien Johnson's side were a credit to themselves and were more than a match for their League One opponents throughout, but they just couldn't convert the openings that came their way.
For their first involvement in the Checkatrade Trophy Damien Johnson named a familiar looking line-up with just a smattering of first team experience amongst the Rovers ranks.
David Raya started in goal, with a back four of Ryan Nyambe, Matty Platt, Scott Wharton and Jack Doyle. In midfield were Connor Mahoney, Willem Tomlinson, Lewis Hardcastle, Joe Rankin-Costello and Connor Thomson, with Lewis Mansell up front. All eleven aged under 21.
Yet the young Rovers were almost caught cold inside the opening 90 seconds. Bobby Grant with a corner from the left, Martyn Woolford with a close-range header which Raya saved well.
But the response from Rovers was impressive, Mansell with a lay-off to Mahoney but his centre into the box was headed wide by the home side with Thomson and Rankin-Costello threatening.
The visitors continued to look the part as Tomlinson, Mahoney and Nyambe combined, the defender's cross from the right was met first time by Thomson but he failed to get his shot on target.
Rovers were quickly back on the attack after Tomlinson cut out a slack pass from Joe Davis, but he passed up the opportunity to shoot, instead finding Mahoney whose cross was blocked for a corner.
But whilst it was Rovers with the better play and possession, it was the hosts who were getting their efforts on target.
Only a fantastic low save from Raya prevented Michael Duckworth from opening the scoring, before a cross from Bobby Grant picked out Woolford but his shot went just past the far post.
Rovers again looked threatening as the half drew to a close, but all of their hard work was undone just seconds from the end of the first half. Mahoney, who had been the pick of the Rovers players, lost possession in the centre of the park and the home side broke quickly through Hunter and he squared the ball across the six-yard box for Cole to fire home.
Trailing at the break, Rovers had an excellent chance to get back on level terms just four minutes after the turnaround.
A lofted pass from Tomlinson saw Mansell beat the offside trap but he snatched at his attempted lob and the ball went wide of target.
Fleetwood responded with a superb drive from Hunter, Raya watching on confidently as the ball narrowly passed the upright.
But as the second half wore on it was Rovers who grew more and more confident creating a host of excellent opportunities.
Mahoney fired just passed the near post after beating his marker all ends up, before Hardcastle fired wide after a Thomson centre.
Then it was Rankin-Costello's turn as he cut inside from the left to shoot, Fleetwood keeper Chris Neal down to his left to save.
The chances kept on coming, the best of which being a 65th minute cross from Mahoney that picked out Mansell at the back post. The forward got his header on target but it was straight at Neal who tipped over.
It was such a one-sided second half that it came as a surprise when Fleetwood almost doubled their advantage with a chance out of nothing. Substitute Ricardo Kip brilliantly controlling a ball over the top before lashing goalwards, Raya with an outstanding save once more.
Johnson's side pressed again as the match entered the closing stages, Tomlinson blazing over the bar after bursting into the box, before substitute Dean Rittenberg was inches wide with a shot on the turn with Neal at full stretch.
The result was tough on the young Rovers, they were more than a match for their League One opponents, they just couldn't turn their chances into the goals they deserved.
FLEETWOOD: Neal, Jonsson (sub Glendon 32 mins), Eastham, Grant (sub Nirennold 68 mins), Bolger, Davis, Duckworth, Hunter, Woolford, Dempsey, Cole (sub Kip 61 mins).
Subs not used: Cairns (GK), Haughton, Deacon, Sowerby.
Goals: Cole 45+2 mins.
Booked: Grant 42 mins, Hunter 85 mins.
ROVERS: Raya, Nyambe, Tomlinson, Mahoney, Wharton (c), Doyle, Thomson (sub Rittenberg 87 mins), Platt, Hardcastle, Mansell, Rankin-Costello.
Subs not used: Fisher (GK), Askew, Travis, Howarth, Grayson, Magloire.
Booked: Wharton 50 mins.