Yes true. We can even say that their defeat in the FA Cup gives them a very good advantage for their forward fixtures. That's why they don't want to compress their main squad with the matches of the FA Cup. That's why regular defeats might work for these teams. This is a long standing system. Maybe there can be such a surprise in the Manchester City-Fulham game today.
I don't think it's luck for Manchester, because after all a big team is required to be able to get every trophy there is, even though the FA trophy is not very prestigious but the trophy should be an achievement for Rangnick at the end of the season, indeed now Manchester is still have hope in champions league but their journey to win a trophy in the champions league is not an easy thing, besides that manchester lowered its main squad against middlesbrough, but instead they suffered a defeat, then how can they be favorites when facing tough teams in the premier league and league champions later?
After being knocked out of the FA Cup the chances of Manchester United are getting a trophy at the end of the season are very small, they certainly will not be able to catch the points collected by Manchester City who are at the top of the standings. In the Champions League Manchester United will have a difficulty faced other big teams. PSG, Real Madrid, Manchester City, Bayern Munich, Liverpool, Chelsea and Juventus are the teams that must be wary of MU.
After suffering a painful loss to Middlesbrough in the FA Cup, Manchester United must get up soon in the next game, they still have a tough task to secure the top 4 position until the end of the season.