A writer of Billboard noted that instead of only trading vocals on the song, the singers delivered "full duet lines". David Saavedra, a critic of the Spanish newspaper El Mundo, found elements of Latin flamenco in "Te Lo Agradezco, Pero No" and noted how it was a proof of Sanz's departure from his early-career material.
A Billboard writer noted that the singers provided more than just vocal exchanges; they offered "complete duet lines". David Saavedra, a critic for El Mundo newspaper, found Latin flamenco elements in "Te Lo Agradezco, Pero No" and observed Sanz's departure from his earlier work.