Nainggolan, 29, and Roma left the Spanish capital emptyhanded as Atletico boosted their hopes of reaching the Champions League knockout round with a 2-0 victory on Wednesday.
Nainggolan, however, reaffirmed his commitment to Eusebio Di Francesco and the high-flying Italian outfit.
"These are lovely words, but I am focused on Roma," Nainggolan told Mediaset Premium.
"I think I made the choice I was happy with last year and the year before. I am happy to represent this team, I live happily off the field and I see absolutely no reason to change that.
"It's an honour for me to wear the armband, following the likes of Francesco Totti, Daniele De Rossi and Alessandro Florenzi.
"Whether I wear the armband or not, I have it within me and feel the desire to always give something more on the field for my team."
Roma lost top spot to Chelsea in Group C and are now second, two points ahead of Atletico with one matchday remaining.