The Blancos have dominated the European scene over the last five years, collecting four continental crowns and a record-breaking three in succession.
They have, however, conquered their domestic division just once during that run – in 2016-17 – with Clasico rivals Barcelona proving to be the most consistent performers.
Zinedine Zidane has walked away from the challenge of trying to replicate Champions League success at home, with Lopetegui handed the reins as he inherits the burden of expectation in the Spanish capital.
Former Madrid striker Morientes told reporters at a La Liga World event in India on what will be demanded from a new regime: “Now Real Madrid's challenge will be to win the league. Because it has been too easy to win the Champions League!
“I know from my experience with Real Madrid that everyone demands you to win every title. And if you don't win whatever cup is at stake, then you will be criticised a lot.
“If you only win the Champions League, then people will say it is not enough. It is very difficult.”
Lopetegui is already in place at the Bernabeu after being relieved of his duties with Spain on the eve of World Cup 2018, with that situation having done few favours to all concerned.
Morientes said when quizzed on how La Roja have been affected by an untimely change in the dugout: “Footballers are professionals. These things can happen. In the first week, everything was like, 'Oh what happened?' but then you need to work hard and concentrate.
“The new coach is Fernando Hierro and he is maybe not the same as Lopetegui because Lopetegui has done a good job for Spain in qualification.
“It is not a big problem for the players. In the end, you need to concentrate on your work. The philosophy remains the same.”
He added: “Maybe it could have been managed in a different way. But also, there are many things at stake.
“Real Madrid needed a coach and they decided it was Lopetegui. They could have maybe held the news for until the end of the World Cup but then if Spain does not do well at the World Cup, it would have been bad for Real Madrid. It [this situation] has no easy answer.”
Spain stumbled their way through a Group B campaign in Russia, but ultimately topped their standings after collecting five points.
Questions have been asked of a defensive unit which has looked uncharacteristically fragile, with five goals conceded so far.
Morientes, who won 47 senior caps during his career, said on the calls for change: “We need to improve the level of the defence.
“But Sergio Ramos and [Gerard] Pique are the best, they are untouchables. The whole team need to defend.”
He added on the criticism aimed at Manchester United goalkeeper David de Gea on the back of some costly mistakes: “It is very difficult to be a goalkeeper of a national team. When you make a mistake, everyone is in front of you.
“It is not easy to be a successor of Iker Casillas. De Gea is a very good goalkeeper but they need confidence.”