The Millers were leading 1-0 thanks to Angus MacDonald's first goal for the club, a third-minute header and were well placed to try and cash in on Derby's defeat at Preston on Tuesday night and increase the pressure on the Rams.
But the game turned on the decision of Bond to send off Crooks for a perceived elbow as he rose and caught Hall in an aerial duel.
It looked an accidental collision of heads with no malice, with Crooks's look of bewilderment speaking volumes afterwards. After the game, Warne said that the player was 'heartbroken.'
It totally changed the course of the game and Boro - seeking a first win in six games - proceeded to dominate.
A fine finish from George Saville after great work from the impressive Neeskens Kebano levelled it up for the Teessiders on 33 minutes and Jonny Howson and Yannick Bolaise hit the bar before the break for the visitors, who went in front early on in the second half when they cashed in on a fumble by home keeper Viktor Johansson which allowed Paddy McNair to set up Chuba Akpom for the winner.
But the talking point afterwards was the decision to dismiss Crooks.
Bond had previous history with Rotherham after dismissing Michael Smith at Hillsborough on March 3 with the decision subsequently rescinded - as was his decision to send off Barnsley captain Alex Mowatt at Wycombe a fortnight later.
Warne, whose side visit Barnsley on Saturday - with their spirits further dented by news of a victory for Wycombe - said: "We're definitely appealing it. I just think we were on the wrong end of a bad decision.
"It was two different games. It was the first 20 minutes when it was even and then it was the other 70-plus with ten men. It could have ramifications beyond this game.
"Crooksy has never been sent off for me before. He's not a dirty player. I want him to attack that ball because that's the way we play. It's a contact sport. He's not maliciously gone to hurt the lad. After the game, he looked heartbroken. It wasn't the face of a warrior who's gone round trying to 'hench' people.
"I've seen it back once in slow motion and it looked ridiculously harsh. Their bench has gone up in a furore and the ref has pulled out a red card. The game takes a completely different turn after that."