Torrential rain overnight and on Saturday meant the fifth tier club’s ground had puddles on the pitch before the game.
The Bantams survived an almighty scare to force a replay after Nat Knight-Percival’s 71st-minute equaliser cancelled out George Fowler’s opener.
Hopkin blasted: “It was dangerous out there and I don’t think the game should have gone ahead.
“There were puddles on the pitch beforehand. Someone could have got seriously injured. It’s a fantastic pitch at Aldershot but the amount of rain that fell made it horrendous to play on.”
Hopkin’s side are 38 places above the National League side in the football pyramid.
But the hosts showed their Football League opposition no respect as Fowler handed them an early 12th-minute lead.
Richard O’Donnell was left stranded when Josh Barrett’s cross found Fowler unmarked at the back post for an easy tap-in.
The Bantams, who sit bottom in League One and who are now without a win in eight matches, roared into life as they searched for an equaliser before the break.
Eoin Doyle and Connor Wood were both thwarted by good saves from Shots’ stopper Will Mannion.
Wood once again went close to beating Mannion, only for the goalkeeper to produce a fine save to tip over his deflected effort.
The visitors thought they had levelled when George Miller beat Mannion, only for the waterlogged surface to stop the ball dead before the line.
Knight-Percival spared the Bantams’ blushes late on when he headed home Jack Payne’s pinpoint corner.
Aldershot almost hit straight back after Bradford’s equaliser, but Adam McDonnell put his free-kick over the bar and the game finished level as Lewis O’Brien’s last-gasp header was well held.
The replay is scheduled for a week tomorrow at 7.45pm.
Aldershot chief Gary Waddock said: “I thought the game could have been called off in the second half. If we’d tried to play our normal passing game, we would have got stuck in the water and a few ducks and swans would have got in the way.”
Aldershot: Mannion, McCoy, Fowler, Osho, Kinsella, Booty (Wanadio 81), McDonnell, Gallagher, Barrett (Howell 58), McClure (Berkeley-Agyepong 76), Rendell. Unused substitutes: Cole, Fenelon, Bernard, Lelan.
Bradford City: O’Donnell, McGowan, O’Connor, Knight-Percival, Wood, Lewis O’Brien, Akpan (Devine 80), Payne (Wright 75), Ball (J O’Brien 64), Miller, Doyle. Unused substitutes: Seedorf, Brunker, Poppler-Isherwood.
Referee: P Marsden (Lancashire).