The former Chelsea and Inter Milan boss guided Real to the Primera Division title last season to end Barcelona's stranglehold although it already faces a task of great magnitude to repeat that achievement given the Catalan team leads Mourinho's side by eight points after just seven matches.
As well as the La Liga crown, Mourinho has also won the Copa del Rey in 2011 and the Supercopa this year, with a two-legged victory over Barca, but he feels he is just a small part of the club.
He told Real Madrid TV: "I'm nothing in the history of
For the players though there is a grand expectation and he lionised their UEFA Champions League efforts when they came back for a late victory over Manchester City.
For Mourinho 'nobility means giving it everything on the pitch', adding: "A Real Madrid player has to die, in a manner of speaking, on the pitch.
"Real Madrid players have to be knackered by the end of the game."
While happy with its Champions League performances so far as well as the Supercopa victory over Barcelona, the Portuguese admits he is less pleased with the stuttering start to the league campaign.
It has already suffered two defeats - the same as the entire 2011-2012 season - although its last three games have garnered seven points with the last game a 2-2 thriller against Barcelona.
Now Mourinho wants his side to maintain such form.
He said: "In the League my team hasn't pleased me: our work hasn't pleased me.
"Now we've entered into a period of growth and stability.
"This team has showed that, when they are doing well psychologically, they are very strong.
"Now we have to get the consistency."
The former Porto boss underlined the galvanising effects of the Barcelona draw and went on: "These humans are special: the demands on them are huge.
"As a coach, I prefer people to criticise me for being aggressive with my words because I try to bring out the wounded pride of my players.
"I prefer that to being quiet, being politically correct, being friendly and going on losing.
"We can't accept this direction
"I'm optimistic because the team is ready to win and win again, draw less and lose even less."
Real Madrid ambassador