Sheffield United finished three points behind Birmingham City (who were promoted in second place) and ten behind league winners Wolverhampton Wanderers.
Reading dominated the match, but Kevin Doyle's shot was blocked on the line; he was later substituted having suffered an Achilles tendon injury.
The game was decided late in the second half when Graham Alexander scored for Burnley from the penalty spot after a foul Steven Thompson by Reading's defender André Bikey.
Goalless at half time, with Reading limited to few chances, a 51st minute strike from 25 yards (23 m) by Martin Paterson put Burnley 1–0 up in the game and 2–0 ahead on aggregate.
[5] The return leg at Bramall Lane was decided by a single goal: Greg Halford's 59th minute header secured a 1–0 win for United on the night, and a 2–1 aggregate victory.
Burnley were playing in their away kit of light blue, while Sheffield United wore their traditional home strip of red and white stripes.
[11][14] After early pressure, United's Kyle Walker struck the first shot on target from 20 yards (18 m) which was saved by Burnley's goalkeeper Brian Jensen.
Two minutes later, a Matthew Kilgallon free kick was blocked by the Burnley wall but not cleared, allowing Howard to shoot from the edge of the penalty area which was saved by Jensen.
He passed to Chris McCann who was tackled, but the ball fell to Elliott whose first-time strike from 25 yards (23 m) flew into the top-left corner of Kenny's net, making the score 1–0 to Burnley.
Two minutes later, Alexander brought down Howard as he ran into the box, but the appeals of the Sheffield United players for a penalty were dismissed by Dean.
Burnley were forced to make the first substitution of the afternoon on 27 minutes after McCann failed to recover from a knee injury he sustained clearing the ball, with Joey Guðjónsson coming on to replace him.
Heading towards half time, the game became patchy with neither side creating clear-cut chances, but on 45 minutes, Thompson's looping header went wide.
Stephen Quinn's run was brought to a halt by an Alexander tackle before Guðjónsson's tap-in attempt was cleared by United's Nick Montgomery.
The resulting free kick was struck into the wall allowing Burnley to break but they failed to score as Montgomery cleared a poor pass from Paterson.
Deep into additional time, Lupoli was booked for a foul on Elliott, and the final whistle was blown, with Burnley winning the match 1–0.
Owen Coyle has done a fantastic, superb job on a small budget, and I'm sure he's looking forward to pitting his wits against the Premier League managers next season".