The Red Devils drew 0-0 with Manchester City at the Etihad Stadium to extend their unbeaten run in the Premier League to 24 matches.
Asked if the undefeated streak shows resilience, Mourinho said: "Of course and today we showed exactly that against a good team, against a strong team that wants to win the match at home.
"Playing with 10 men, without any midfield players to make any kind of change because I didn't have any midfield players on the bench. I played Tim Fosu-Mensah in that extreme situation.
"The team is in trouble, the team has a lot of problems and to play a big derby like this one the way we did shows resilience, shows big character from the players.
"Today a lot of people were focused on the difference of points between us and Man City but I think some people forgot to look at the distance to Liverpool and this point can be a very important point for us.
"Twenty-four matches unbeaten in the Premier League is not the same as 24 matches unbeaten in another league. It means a lot. That desire means a lot for everyone."
United's last loss in the league came against Chelsea in October.