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.
According to a Billboard writer, the singers did more than swap vocals; they offered "full duet lines". David Saavedra, a critic for El Mundo newspaper, detected Latin flamenco influences in "Te Lo Agradezco, Pero No" and observed that it showcased Sanz's evolution from his earlier material.