The Portugal international joined Madrid from Benfica in 2011 but has faced a battle with Marcelo for first-team football over the past two years and has made just 26 league appearances in the last two seasons.
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And Coentrao believes that the extra backing from both the club and supporters has given him the confidence to continue his career in the Spanish capital as they aim for a possible six trophies this season.
"We played a good game and gave everything to win. The trophy is deserved," he told Marca after beating Sevilla 2-0.
"We're going to fight for all titles. Now the work for the other five begins. When Madrid play, they play to win.
"I'm in a better moment than when I arrived. I have the confidence of the fans and so it's easier.
"I hope to have continuity. This is my fourth year in Madrid, I'm enjoying it and I hope to continue. I feel I'm valued more."