United manager Alex Ferguson told a news conference the Premier League club had written to UEFA asking them to overturn Fletcher's semi-final red card but were not optimistic of success.
UEFA said it was not likely that its disciplinary body would lift the punishment when it met to discuss the matter on Monday as the only grounds for appeal were in a case of mistaken identity, which was not an issue with Fletcher.
"We understand that United have to do everything they can possible and we are sympathetic to their concerns but the rules are very clear; his identity was not mistaken," a UEFA spokesman said on Friday.
"They have the right to protest and they may base their argument on sporting grounds. But it is unlikely the decision will be overturned based on the rules."
Fletcher was sent off for what looked a fair challenge on Arsenal's Cesc Fabregas late in Tuesday's semi-final second leg at the Emirates, which United won 3-1 to progress 4-1 on aggregate.
"We have written a compassionate letter to UEFA," Ferguson said earlier on Friday. "We understand the system and honestly believe the referee made the right decision at the time. From his angle and from where I was, I thought it was a penalty myself.
"But we're not optimistic at all. We have to do it for Darren and in fairness to Darren. But, sometimes, in these situations when everything is addressed, you never know.
"He's quite a placid lad, he's not an emotional boy, he accepts it although it's disappointing for him, obviously. He takes great credit for the way he handled it all."
United will play Barcelona in the final in Rome on May 27, when the Spaniards will have two players suspended - Daniel Alves and Eric Abidal, who was sent off in Wednesday's 1-1 draw at Chelsea that put them through on the away goals rule.
United will be without England defender Wes Brown for the rest of the season due to a foot problem. Brown has not played since January.
"He has had a little setback during the week and it's knocked him back," Ferguson told Friday's news conference. "The fact the season is coming towards the end makes it difficult for him but with Gary (Neville) back we're not bad."
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