The Red Devils are currently down in sixth position in the Premier League table, but they will take on Southampton in the final of the League Cup later this month, in addition to playing both FA Cup and Europa League fixtures.
Speaking at his pre-match press conference ahead of the first leg of the last-32 Europa League tie at home to Saint-Etienne, Mourinho has conceded that the growing fixture list is a concern.
"We cannot choose competitions at Manchester United. We know that our situation is really complicated, that the Europa League is a competition where we play on Thursdays and that makes it even more difficult, the accumulation of FA Cup, League Cup, match postponements, it's really hard and if we progress in the competitions we will be injured," Mourinho told reporters.
"We play competitions to win and I think it's also a good way to give a team experience and international experience is always a plus. Europa League is not a competition we want to play but we show it respect.
"If you ask me do I want to progress in the Europa League I tell you yes. We don't throw away competitions, we are going to play to win and to progress. It's even harder, the fact that the match against [Manchester] City is postponed."
"If we win against Blackburn the match against Southampton will also be postponed because the quarter-finals are played the same week the Premier League plays. It's going to create us many, many, many problems."
Man United do not return to Premier League action they host Bournemouth on March 4.