Snapped up after last season's treble-winning exploits with Inter Milan, Mourinho's arrival as coach at the Bernabeu has raised expectations he can end Barcelona's two-year reign as champions.
GEAR:Get your new Barcelona and Real Madrid shirts here. Free delivery on orders over £50
While his new team were struggling to click in Mallorca, Pep Guardiola's well-drilled outfit banged in three goals thanks to Lionel Messi, Andres Iniesta and David Villa.
Real Madrid's Argentine striker Gonzalo Higuain was denied three times by home goalkeeper Dudu Aouate and Cristiano Ronaldo spurned a great chance as the visitors upped the pressure.
Mourinho's new signings Mesut Ozil, Sami Khedira, Angel Di Maria, Sergio Canales and Ricardo Carvalho all featured but despite a frantic finish Michael Laudrup's Mallorca were worth their point.
"We are a team in construction. I would like us to have had three points... but it's not a dramatic situation," Mourinho told reporters. "On a positive note we conceded very few chances and had no problems at the back.
"The negative point is the result. I'm disappointed that with the number of chances we created we didn't score.
"When you aren't at your best you have to do two things, defend so your opponents don't score, and take your chances. We deserved to win," added Mourinho.
"We were good tactically and very good in defence," Real Madrid's keeper and captain Iker Casillas told Spanish television.
"We did well and little by little will get better. The ball just did not want to go in."
"We still lack a little continuity in our play but this will improve as the season progresses," Guardiola told reporters.
Xavier Prieto raced on to Joseba Llorente's backheel to score after 57 minutes, making them the only promoted club to win in the opening round of matches.
