The full-back believes he is reaping the benefits of backing from the coaches and supporters, and is targeting a clean sweep of trophies this season
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 managed just 26 La Liga appearances in the last two seasons.
The 26-year-old was reportedly close to joining Manchester United at the end of last summer's transfer window but has since re-established himself in los Blancos' first-team plans under Carlo Ancelotti and started the Uefa Super Cup win on Tuesday.
And Coentrao believes the extra backing from both the club and supporters has given him confidence to continue his career in the Spanish capital as they aim for a staggering six trophies this season.
"We played a good game and gave everything to win. The trophy is deserved," he was quoted as saying by Marca after the 2-0 win over Sevilla.
"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."