The flamboyant Portuguese was poached from Inter Milan at the end of last season to try to wrest the La Liga title from Real's arch-rivals Barcelona and lead the club to a 10th European cup triumph.
Their record this season is six wins and two draws in all competitions, although until Sunday they had struggled to convert an abundance of chances and had drawn whistles from some of their demanding supporters at the Bernabeu.
"We are not the best team in the world yet for having beaten Depor 6-1," Mourinho said at a news conference.
"We are under construction and neither the result nor the applause of the fans makes me think our work is done," the 47-year-old added.
"The work continues. I am very calm. We have a lot to do and a lot of work.
"I have the confidence of my president and I have the confidence of the board."
Mourinho had a difficult relationship with the Italian media during his time at Inter and has already upset some Spanish journalists who have complained he does not allow them enough access to the players.
He gave a prickly response on Sunday when he was asked whether the performance against Depor was a good response to those who questioned his abilities.
"If you have doubts about a coach who has won what I have then you have to explain what qualities a coach should have to have the right to work in your country," he said.
"You have to tell me if I have to have won three Champions Leagues and seven domestic league titles.
"I have two Champions Leagues and six domestic league titles. Is that enough to have the right to work here? If so, great. I'll continue with my work."
Mourinho won the Champions League with Porto in 2004 and Inter last season. He also won two domestic titles with Porto, two with Chelsea and two with Inter.
