The FA Cup means a lot to Manchester United and I'm sure the fans value it highly caused by it was also helping them all to be even superior compared to those three clubs at the same time. I believe that all of the United fans are delighted with the result. Despite their struggles in the EPL, United was eventually able to qualify for the Europa League the following season which is good enough rather than got nothing.
United can still compete in the Europa League to replace Chelsea, which has finished behind Tottenham.
Of course, the trophy that MU currently gets is like a special trophy for them. We know that MU has failed to win EPL title for more than a decade. MU won the last FA Cup it has been 8 years ago they won the title, before this season. That why i aggree with you, if the winning match and get trophy over City was a special title for MU, even though they were not getting EPL champions, but preventing City from doubling the domestic title was very important. Because this is also about the derby match, if MU loses again to City, then MU will cause more pain to the fans.