The 24-year-old left-back, who joined Forest in July 2015 from Spanish side Cordoba, made 35 appearances for the Reds and was out of contract.
Warburton told BBC Radio Nottingham: "From the first day I was in the hot seat he's been a perfect professional and worked very hard.
"I thank him for all of his efforts and wish him the very best for the future."
Pinillos injured his knee ligaments in December 2015 and did not feature again for the Reds until November 2016.
His only goal for Forest was an injury-time equaliser in a 2-2 draw with local rivals Derby County in March.
The Reds avoided relegation to League One on goal difference only on the final day of the season.
Nottingham Forest defender Dani Pinillos is to leave the club, says manager Mark Warburton.