UEFA banned the Portuguese on Tuesday after allegations that he had engineered deliberate red cards for two of his players in a Champions League match.
Xabi Alonso and Sergio Ramos picked up yellow cards for time-wasting which resulted in them being sent off at the end of their 4-0 win away to Ajax last month.
"I see this punishment as a medal," Mourinho told a news conference.
"I'm not going to change. My grandmother died a long time ago but I remember what she told me as a child. 'If they are envious of you, you should be happy,' and this has happened to me.
"I'm pleased there is one rule for Jose Mourinho and one for the other coaches. It's a historic punishment for me. Following the line of my old grandmother, it's a medal not a punishment.
"I can't leave the technical area, others can. I can't pick up a ball an adversary wants, others can. I can't speak with the fourth official, others can. They are medals so, no worries."
After the Ajax game, Spanish media reported the Real players had acted on instructions from Mourinho. They said the message was passed from Mourinho to reserve goalkeeper Jerzy Dudek and on to first-choice keeper Iker Casillas.
Spanish television showed Dudek talking to Casillas with hands covering their mouths and then Casillas was shown doing the same with Ramos.
The sendings-off mean Alonso and Ramos will serve automatic one-match suspensions in the final group game against Auxerre, which is a dead match for Real as they are assured of first place in Group G and qualification for the last 16.
Both players had accumulated two yellow cards in the group stage before they were sent off and a further yellow card in a subsequent game would have meant a one-match suspension during the knockout rounds.
UEFA fined the club, Mourinho and the four players involved. The second match of Mourinho's European ban has been deferred for a probationary period of three years.
