Dawson got his marching orders following a late challenge on Blades striker Steve Kabba with seven minutes to go.
Paul Hart said: ''We'll be asking the FA and the referee to have a look at the video. That's all we can do.''
Dawson was this week included in the First Division team of the season but picked up his first senior red card at a key stage of the campaign.
Hart added: ''To be fair it is a foul, but I think that was a first Michael had committed all day. The stats will stand that up. Obviously, Michael is very disappointed."
Forest captain and man of the match Des Walker has told him to keep his head up and he thought the red card was very harsh.
Even Blades boss Neil Warnock came out and said he thought the challenge wasn't malicious. He said: ''He over-committed himself for the tackle and couldn't stop Kabba. As a big lad he couldn't pull out."
Referee Mark Clattenburg issued five yellow cards on Saturday taking his seasons tally to 131 and Dawson's sending off was Clattenburg's seventh in only 34 games.
It is believed he will be recinding Michael Brown's yellow card for his goal celebration after the video showed he had not jumped over the advertising hordings and hopefully Dawson's will be cut-down to only a yellow card.
The second leg will be played on Thursday 15 May at Bramall Lane. Just a reminder to Forest fans - away goals do NOT count in the playoff semi-finals.