The Yellow Submarine gained promotion from the Segunda Division in the 2019-20 campaign, and they have finished 12th, 17th and 14th in their last three full seasons in the top flight.
Cadiz have enjoyed their best run at this level since the early 1990s, but their relegation to the second tier has now been confirmed ahead of their final match of the season.
Mauricio Pellegrino's side needed to beat Las Palmas on Sunday to take their fight to the final weekend, but they were held to a goalless draw on home soil.
Cadiz entered the match off the back of successive 1-0 wins over Getafe and Sevilla, with their supporters dreaming of a great escape late in the campaign.
However, 17th-placed Mallorca, who drew 2-2 with Algeria on Sunday, are now four points ahead of 18th-placed Cadiz in the table with just one game of the season left to play.
A tough season has seen El Submarino Amarillo win just six of their 37 matches, drawing a league-high 15 times and also suffering 16 defeats, while they are the lowest goalscorers in the division on 25.
Cadiz have been relegated down to the Segunda Division alongside Granada and Almeria and now only have pride to play for in their last game of the season against Almeria next weekend.