Real went into the halftime break 2-0 down before Gonzalo Higuain inspired a second-half comeback.
Mourinho said: "I liked the team's mentality. They did not want to lose. I always tell my players that friendly matches do not exist, that pre-season matches are used to make a lot of changes and that winning isn't what counts.
"I do not like the word 'friendly' in football. I can tell the players want to win every match. There were moments I didn't like in both of our matches, but that's logical because we are still working and learning and there are many things to iron out.
"That said, there were also a lot of things I did like, such as the second half of today's match. I liked how we played on defence, how we pressured, how we played the ball and how we managed to score."
The 'Special One' also had special praise for striker Higuain.
"Gonzalo Higuain is a top forward. He scored two goals, which is quite important to a forward.
"What I liked most were his movements on the pitch, which were those of an intelligent forward. He makes the game easy for other attackers because he plays from behind and opens up a lot of ground."