Fletcher was sent off for bringing down Cesc Fabregas in the area during's United's 3-1 victory at Arsenal in Tuesday's semifinal second leg. Arsenal scored on the resulting penalty.
United lodged an appeal on compassionate grounds, but Ferguson said Friday he did not have high hopes that it would succeed.
"We have written a compassionate letter to UEFA. We understand the system and I honestly believe that the referee made the right decision at the time. I thought it was a penalty," Ferguson said.
"I'm not optimistic at all. We have to do it for Darren, really. I don't think it will be overturned."