Madrid lifted the Copa del Rey and Champions League last term but had a disappointing league campaign as they finished third, behind Barcelona and champions Atletico Madrid.
And Ronaldo is now determined to pry the league title from Diego Simeone's side, while retaining the European crown and domestic cup.
"It was a fantastic year. We won the Champions League, we won La Decima - the trophy that Real Madrid had been looking for a lot," he told the press.
"So this season we’re going to try to do the same, to win the Champions League again and to win La Liga."
The 29-year-old added that he aims to improve his performances by breaking his own goalscoring records, having thus far failed to improve on his record of 46 in 38 league games in 2011-12.
"In terms of individual achievements, I'm going to try to break my own records," he continued. "I know it's tough but I'm going to try."
And the 2013 Ballon d'Or winner also hopes that his son can follow in his footsteps by becoming a footballer.
"I would love Cristiano to be a football player but these matters I cannot decide," he remarked. "I made sure to bring him here because I just love being with him, playing with him."