SEE MATCH PHOTOS
And despite having 70 minutes to find an equaliser, Leeds were unable to spare Miller's blushes as they bowed out in the last 16.
"I don't think either set of players really believed what had happened," said Leeds boss Ian Selwyn.
"When Brad put the ball through, both sets of players turned around to jog back to halfway because they expected the keeper to pick the ball up.
"And then suddenly, I'm thinking, 'that's gone in. How the hell has that gone in?'
"It was a dreadful mistake and unfortunately that error was the difference."
Miller was in fine form during Leeds’ impressive 2-1 win over New Ireland Wood last Sunday but was soon cast as the villain following Oakwood’s first-half opener.
The visitors huffed and puffed for long periods but Richard Black and Dave Woolman both missed opportunities to drag the visitors level.
"It was a close and competitive game between two equally matched sides and perhaps we cancelled each other out," added Selwyn.
"Oakwood had the better of the first half but we had the better of the second and I think our fitness showed in the closing stages.
"But you have to give great credit to Oakwood because they put their bodies on the line even when they were out on the feet.
"I've no complaints about the result. I'd like to wish Oakwood every success in the competition and hopefully they can go on and do well.
"We were treated fantastically well by everyone and we’re very grateful for the hospitality."
Oakwood joint-manager Ric Blank told JC Sport: "As expected, it was a full-blooded, epic cup tie played at a million miles per hour at Parmiters.
"It was a gripping game we thoroughly deserved to win. We controlled the first half and were disappointed not to put the matter to bed in the second half with the number of chances we created.
"In the second half Leeds tried to turn up the pressure but never really got going. Adam Levine was imperious at the back against Woolman and did not give him a sniff.
"Kintish was causing all sorts of problems for the Leeds back four with his running and determination - he never let them settle for a second and they couldn't handle him.
"The team spirit was outstanding on Sunday and the one time Leeds did get round the back, Josh Rubin pulled off two miraculous blocks to stop Leeds from equalising.
"We wanted it all over the park yesterday and refused to be bullied, showing great courage to keep the ball moving all over the park - especially in the first half.
"We know there are some great teams left in the competition and Redbridge, Manchester Maccabi and my old club South Manchester are overwhelming favourites, but we are just looking forward to being in the next round and hopefully another chance to test ourselves against a good side.
"In the meantime we turn our attention back to the league and a huge game at home to Southgate Harmen B. Southgate beat us last season and we are desperate for revenge this time around."
