The 27-year-old is on loan from the Sky Bet League One club until January 1.
Under the terms of the temporary move, Hall was not allowed to compete in the FA Cup.
It is a common clause, as an appearance for United would mean Hall could not play for his parent club if they had a run stretching into the new year.
United checked to see if that was still the case before their first round tie with Gateshead, but it was turned down.
But with the Shrews out of the competition following a 3-0 defeat to Walsall last month, there were hopes the barrier would be removed.
Following the first round replay victory at Gateshead on Thursday night United tried again, but Shrewsbury stood firm.
Mickey Lewis, United’s assistant manager, did not understand the decision, but felt there was nothing they could do.
“I’ve no idea (why) to be honest, but it’s their decision and you can’t question it,” he said.
“It’s their prerogative, he is their player.
“It’s a shame because Asa is a really good player and especially since he came off the bench against Mansfield, he has done really well and been one of our best performers.
“It’s a bit of a blow, but as with last Thursday we just have to get on with it.”
Hall would have been a very welcome addition to a squad which has been hit very hard by injuries.
There was some good news before the bus left for north Wales yesterday.
Danny Rose and Dave Kitson, who were forced off with minor knocks at Gateshead, should be fine to keep their places in the starting line-up.
Both Michael Raynes and Johnny Mullins missed out last week after picking up hip and knee injuries respectively.
United could have to do without the centre backs again, although Lewis felt Mullins was an outside bet of making the squad.
He said: “I think it will more or less be an identical squad, perhaps with one added from last week.
“Johnny Mullins has got a chance of making it.”
Wrexham player manager Andy Morrell’s selection problems centre around who to leave out.
They have won their last three games, but have Brett Ormerod and Joe Anyinsah back after injury, while fellow forward Andy Bishop is available after suspension.
TONIGHT’S SQUADS Oxford Utd: from Clarke, Bevans, Hunt, Newey, Lynn, Williams, Davies, Rose, Ruffels, Kitson, Constable, Smalley, Marsh, O’Dowda, Long, Lee, Shama, Mullins, Crocombe.
Wrexham: from Coughlin, Hunt, Clowes, Parle, Tomassen, Colbeck, Evans, Carrington, Cieslewicz, Morrell, Bailey-Jones, Mayebi, Ashton, Clarke, Ogleby, Ormerod, Bishop, Anyinsah.