Paul Charnley's side trailed 4-0 from the first leg and conceded a goal to Stuart Ellis in the 34th minute to lose the match 5-0 on aggregate.
The Shropshire side will face Boldmere St Michaels in the Final at Walsall FC. Boldmere beat Highgate United 3-1 tonight to record a 5-1 aggregate victory.
Former Sky Blue Paul Hall scored twice for Stratford Town in a 4-0 win over Causeway United, whilst former City youngster Ange Lourougnon scored for Barwell in a 2-1 win over Coalville Town.
Nuneaton Griff won the Coventry Telegraph Cup Final with a 4-3 victory on penalties at the Ricoh Arena. They beat fellow Midland Combination Premier Division side Coventry Copsewood on spot kicks after the match finished in a 1-1 draw.