The 54-year-old was appointed head coach of the Spanish outfit on January 19, but was unable to steer the club away from the relegation zone, with Betis finishing bottom of the division.
It was revealed earlier this week that Calderon had left his position as manager of the Spanish side, but he believes that the team will rise again.
"I leave sad, disappointed and appreciative. Sad for not having saved the team, which I feel responsible for, and thankful for the fans, the players and the club. Given the results, it is logical that I won't continue. I will support the club like a shareholder, for it to return to the Primera as soon as possible," Inside Spanish Football quotes Calderon as saying at a press conference.
"I came in a situation where I came and I have given my life from the inside out to Betis, I didn't want to be on the outside. We already know what football is. A coach needs maximum support, and whoever comes now should have it.
"I don't have recommendations as to who should fill my position, they will look for the competent people. I have already passed on a report player by player. The template isn't so bad but clearly some things have to change. My worst moment was the descent. The worst thing was to bring joy to the fans and then take it away."
Betis have not yet appointed a new boss.