The Portuguese added that Barca still remain "a great team" despite failing to retain their La Liga and Champions League crowns last season.
"We are talking about Barcelona and Real Madrid, two great teams," Mourinho told AS. "Pick any other team in the world, and they would not finish in the top two in La Liga.
"And that's exactly why I joined Real Madrid. Because it's not easy to challenge Barcelona. It's very hard to be successful in this competition.
"Barcelona's era of winning consecutive Liga titles is over, but their cycle has not come to an end yet. They are still a great team and so are Madrid."
Mourinho further said that La Liga is the toughest league to win at the moment.
"Life's much easier in any other league," he said. "Any league where you are not locking horns with Barcelona is easier.
"Barca are the main reason why Madrid got to where we are now, because they set the bar very high."
Madrid have picked up four points from three matches in La Liga so far this season.