"Having spoken to the referee's chief and to the referee himself, their feeling is that the decision wouldn't be altered," Southgate told the club's official website.
"Whether or not there is intent is no longer considered, it's about whether a challenge puts the opponent in danger.
"At no time has anybody suggested Mido intended to do what he did, but unfortunately it is perceived as dangerous play because he caught the lad.
"We're not very happy about it but I can see why the referee has sent the lad off under those rules. But a three-match ban is very harsh.
"I believe the referee gave the red card when he saw the injury, because he was bleeding on the top of his head, but it was very difficult to assess that he wanted to hit him on his head, I don't think so."