Los Blancos began 2017-18 where they left off last season, earning a convincing two-legged victory over their arch-rivals to lift the trophy for a 10th time.
Pique admits that, for the first time in his near-decade long stint at Camp Nou since returning from Manchester United, it is the capital club who have the clear advantage.
"The season is very long and there is room for improvement," Marca quotes him as saying. "But in nine years at Barcelona this is the first time that I have felt we are inferior to Madrid. It is true that they won the Champions League last year, but we came here and won not long before that.
"We are not in the best moment as a team or a club. We must remain as close as possible and try to keep paddling forward. It is important for us to live with the defeat and accept that Madrid were better."
Madrid came out on top 5-1 winners on aggregate in the curtain-raising tie of the new Spanish football season.