At the time United were a goal to the good, after Latics defender Sean Gregan had headed into his own net from an Ian Morris cross.
Byrne was shown a straight red for a challenge on Chris Taylor after 61 minutes, and United's Taylor was shown a second yellow shortly afterwards.
A series of impressive stops from Iron keeper Joe Murphy looked to have earned the home side a win which would have kept them top, but four minutes into second-half stoppatge time Gary McDonald smashed the ball home following a goalmouth scramble.
Adkins refused to comment on Deadman's officiating, instead choosing to focus on the determination shown by his side after the red cards.
"I have nothing but praise for the way my team played when we were down to nine men," he insisted.
"They went to war out there. They put their bodies on the line and showed just what sort of spirit we have at this club.
"To concede an equaliser so deep into stoppage time was cruel, but in any case it should have been a free-kick to us following a foul on our goalkeeper.
"We knew that Oldham were a good team, and for 45 minutes we could not get the ball off them.
"But we got the goal we wanted early in the second-half and then were unable to build on it because of what followed."
The Latics had been the better side even before Byrne was sent to the dressing room, and John Sheridan felt his side's display merited at least the point they took back to Lancashire.
"I thought we were much the better team, even when it was 11 v 11," he insisted.
"I thought we were unlucky to have Paul Warne's header cancelled out in the first half for off-side, but then it was one of a number of funny decisions which went on out there.
"I am sure that this match will be remembered for the red and yellow cards, but I thought we played well and certainly deserved at least a point.
"We showed character to keep going right until the bitter end. It's not easy to play against nine men, with Scunthorpe not interested in doing anything else but defending."