Players from both sides surrounded the officials after substitute Jamie Mackie’s last-gasp winner.
Oxford took a goal-kick quickly and it led to Mackie hitting the winner. Bradford’s players protested that the kick was incorrectly taken by Simon Eastwood.
Bowyer said: “I’ve never seen anything like it in all my time in football – and I’ve obviously spent a long time, first watching my dad (Ian) and then as a manager.
“I still can’t understand what’s gone on. Our lads believe the officials have got it wrong – and to allow chaos to break out like he (referee Andy Davies) did was ridiculous.
“We looked like we were going to get a valuable point, if not three, and then chaos ensued.”
Both sides struggled with tough conditions. The Bantams defence battled hard but Jacob Butterfield blasted over for the visitors.
Karl Robinson’s side regularly got in decent portions but failed to work Richard O’Donnell. Gavin Whyte fired over before James Henry hit wide. After the break, Adam Chicksen’s clearance fell to Whyte who missed the target.
Just after the hour, O’Donnell produced a fine save to keep out Henry’s free-kick.
Anthony O’Connor headed Butterfield’s corner over as the Bantams pushed for a late winner. Cameron Brannagan went close before Mackie’s controversial volley sent Bradford to the bottom and took Oxford out of the drop zone.
Oxford United: Eastwood, Long, Nelson, Dickie, Ruffels, Kashi, Brannagan, Whyte, Graham (Browne, 63), Henry (Mackie, 70), Sinclair. Unused substitutes: Stevens, Garbutt, Hanson, Mousinho, Sykes.
Bradford City: O’Donnell, Caddis, O’Connor, Knight-Percival, Chicksen, Clarke, Anderson, Akpan, Butterfield, Ball (Miller, 56), Doyle. Unused substitutes: Wilson, Payne, Patrick, Staunton, O’Brien, Wright.
Referee: A Davies (Hampshire).