"This is the press conference that I never wanted to hold," Realbetisbalompie.es quotes him as saying.
"I want to thank the president [Miguel Guillen] and many other people - I can certainly start by thanking every player Roberto, David and I have worked with since 2010. Thanks for all the work you've done with us.
"We've gone through bad times and had to overcome them but now, unfortunately, we could not resolve this situation. I would ask you all to show the new coach the same love you showed me. Thanks to everyone."
Garrido, who will take charge until the end of the season, led Villarreal into the Champions League in 2011.