The Spanish coach was given his marching orders after a defeat to Norwich City on Saturday.
Everton were on a run of one win in the past 13 league matches, which has seen them slip into a relegation battle.
In his statement, Benitez said: "We knew it wouldn't be easy, and that it was a big challenge, both emotionally and in terms of sport. My love for this city, for Merseyside and its people, made me accept this challenge, but it is only when you are inside that you realise the magnitude of the task.
"From the very first day, my staff and myself worked as we always do, with commitment and full dedication, we didn't only have to get results, but we also had to win over people's hearts. However, the financial situation and then the injuries that followed made things even harder.
"I am convinced that we would have been better once the injured players were back and with the arrival of the new signings.
"The road to success isn't easy and sadly, nowadays in football there is a search for immediate results and there is always less and less patience; unfortunately circumstances have determined the results and it won't be possible to continue this project.
"In any case, thank you to the Board, to the staff, to the players, and to those fans who have supported us during this time. My best wishes for EFC. Rafa Benítez."
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