After a goalless 90 minutes and extra-time period against Morocco on Tuesday, 2010 champions Spain were dumped out on penalties in a huge shock.
Luis Enrique's contract was due to expire at the end of the tournament in Qatar, and the Royal Football Federation (RFEF) confirmed on Thursday he would not stay on as head coach.
The RFEF subsequently announced Luis de la Fuente is set to take over the role, having previously been in charge of Spain's Under-21 side.
In a statement released on Thursday, Luis Enrique spoke of his gratitude to those who had helped him in his time as Spain boss, while imploring supporters to get behind De La Fuente.
"It all started four years ago and how fast time has passed," Luis Enrique said in a Twitter post.
"I can only be super grateful to those who signed me twice (president Rubiales and sports director Molina), to all the RFEF employees with whom we share experiences of all kinds, of course, to the players who have been exemplary in their behaviour and faithful to the idea raised.
"I'm sorry I couldn't help you more.
"It has been very special to be a part of this.
"Last but not least, to the fans who have uniformly conveyed their support to us at all times and especially in the most delicate ones.
"It's time to say goodbye and in these cases just a little reflection... what the team needs is support in all its meaning so that Luis de la Fuente achieves everything he wants."