Published Tuesday, 25 September 2012
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David Cushley scored the crucial goal just before half time at the Showgrounds.
Cliftonville manager Tommy Breslin said the team missed plenty of chances.
"Very disappointed, especially the way we went out, I thought you know, no complaints, Ballymena were hungry from the first whistle," he said.
"The movement was a lot sharper, so good luck to them in the next round," he added.
Meanwhile an edgy performance saw Crusaders also go through to the semi-finals as they beat Bangor 2-1.
Jordan Owens and Paul Heatley put the home side in front before Thomas Lambe pulled one back.
The other two ties of the round did not survive the heavy rainfall that's been battering Northern Ireland this week.
Glentoran will now play Linfield in a rescheduled Big Two clash next Monday, while Donegal Celtic take on Lisburn Distillery.
Both games kick off at 7.45pm.
Tuesday's County Antrim Shield QF results:
Ballymena United 1-0 Cliftonville
Ballymena Utd: Cushley
Glentoran P Linfield
Donegal Celtic P Lisburn Distillery
Crusaders 2-1 Bangor
Crusaders: Owens, Heatley.