A cup tie ended in controversy after a team losing 2-0 rejected replacements for the injured referee, forcing the match to be abandoned on 83 minutes.
Altrincham's chairman said they should be awarded the win after Colwyn Bay turned down a replacement from the crowd, claiming he had been drinking.
An offer from Robins coach Ian Senior to run the line in the FA Trophy tie at Colwyn Bay was also rejected.
"I hope common sense prevails," Alty chairman Grahame Rowley told BBC Sport.
"We hope we don't have to come back for seven minutes. We were dominating. They should award the game to us."
Colwyn Bay expect the game to be replayed in full on Tuesday, and manager Frank Sinclair told BBC Radio 5 live's Non League Show: "You can't just have any Tom, Dick or Harry come in and finish the last 10 minutes of the game.
"There was no-one on our side that had any officials' badges. One of their staff said he would see the rest of the game out with no qualifications. It's human nature that if there was a big decision to make, we wouldn't have got it.
"I've been within my rights to not agree to carry on."
A club spokesman added: "You can't blame us for the referee being injured. FA rules are very clear. It has to be replayed."
The Conference North sides must now wait for the Football Association to decide whether the tie must be replayed, the remaining seven minutes played, or whether Altrincham will be awarded the tie.
The FA told BBC Sport on Saturday evening that it could not comment until receiving the full details.
The referee injured his calf with seven minutes of normal time remaining, with no designated fourth official available.
"There was an announcement asking if there was an official," Rowley said. "We put forward a fan [to run the line], who is a level-five qualified referee. Colwyn Bay turned that down."
A spokesman for the Welsh club confirmed that option was turned down over concerns the man had been drinking.
Rowley added: "We put forward our assistant to run the line. They refused that. They would not put forward anyone themselves. It's a poor show."
James Walshaw and Greg Wilkinson had scored Altrincham's goals in the third qualifying round match.