Charlton will play League One football next season after being knocked out of the play-offs by Shrewsbury.
Carlton Morris’ second-half goal made it back-to-back 1-0 wins for the Shrews, who will play either Rotherham or Scunthorpe in the final.
Controversy surrounded the Addicks’ second leg defeat, though, as Morris should have been sent off for a blatant elbow on Patrick Bauer before Lee Bowyer’s side had a stonewall penalty appeal turned down.
Bowyer made three changes to the side that lost the first leg with Anfernee Dijksteel, Joe Aribo and Tariqe Fosu replacing Ahmed Kashi, Ben Reeves and Stephy Mavididi.
Playing in front of a raucous crowd, Charlton’s stars seemed nervous - and it told with their minimal threat in the opening 20 minutes.
Shrewsbury came close to scoring on 11 minutes when Morris’ cross found Alex Rodman, whose near-post effort was saved by Ben Amos.
Charlton had a brief sight of goal shortly afterwards with wayward volleys from Fosu and Josh Magennis.
Morris, who was criticised by Bowyer for his dangerous fouls on Jason Pearce and Ezri Konsa in the first leg, was lucky not to see red again. The Norwich loanee elbowed Bauer on the left-side of his head, but nothing was given.
As Shrewsbury’s defence started to drop, the Addicks had their best chance of the half. Jake Forster-Caskey picked out Nicky Ajose’s run with an inch-perfect 50-yard pass, but the striker, under pressure from Aristote Nsiala, was denied by goalkeeper Dean Henderson.
The visitors then had a huge claim for a penalty turned down by Simpson after Mat Sadler blocked Joe Aribo’s cross-shot with his arm. Bowyer and Johnnie Jackson were incensed on the touchline - and they had every right to be.
Charlton’s misery was nearly compounded just before the break when Rodman raced through on goal, however fortunately for the Addicks, Amos saved the close-range strike with his legs.
Shrewsbury came out firing at the start of the second-half. Bowyer’s men lost possession in their own half and Nolan picked the ball up and dragged an effort just wide.
Bauer and Pearce then had to be at their best to cut out dangerous crosses.
Shrewsbury’s pressure paid dividends when they went in front on 58 minutes. Shaun Whalley, the supplier of those earlier menacing crosses, pulled the ball back to Morris, who slotted it past Amos.
Charlton responded by bringing on Mavididi and Sullay Kaikai in quick succession, but it didn’t change their ineffectiveness going forward.
Charlton had a rare sniff at goal when Henderson dropped a Forster-Caskey corner and Aribo’s shot deflected wide with 11 minutes to go.
Henderson was called into action just two minutes later after pushing Forster-Caskey’s long-range strike away from goal.
Amos stopped the Shrews from doubling their lead in injury-time after somehow denying Stefan Payne from close-range.
Ultimately, the Addicks failed to create enough chances over the two legs to warrant a trip to Wembley. The 20-year wait goes on…
Charlton XI: Amos, Dijksteel (Sarr 86), Bauer, Pearce, Dasilva, Fosu (Kaikai 62), Konsa, Forster-Caskey, Aribo, Magennis, Ajose (Mavididi 59).
Subs not used: Phillips, Kashi, Reeves, Zyro.
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