While Madrid have claimed two Champions League trophies in three seasons, the Spanish capital club have not won La Liga since 2012.
Bitter rivals Barcelona have dominated in that period with three titles in four seasons and Morientes - who won three Champions League crowns during his illustrious time at the Santiago Bernabeu - said domestic glory is paramount for Madrid.
"I think Real Madrid's number one objective before the season started was to win La Liga and it still is," Morientes told Marca.
"If they can win the Champions League on the way then that's even better, as it's the competition everyone wants, but five years without winning the league is not good for Real Madrid, for both the fans and the club.
"That is why it is the main goal."
Zinedine Zidane's men are on track to end Barca's dominance, with Madrid a point clear atop the table, having played two fewer matches.
Madrid travel to Osasuna on Saturday.