Las Palmas are 15th in the standings with six points and Marquez's last game in charge was a 2-0 home defeat by Leganes on Sunday.
Marquez had never coached a top-flight side before landing the job in July after leading the club's reserve team to promotion.
"We all thought it was the best option at the time and I would agree to it 80 times out of 100 but as the days went by I began to feel out of place," Marquez told reporters.
"We can't deny that everything happened very quickly and in a hurry. I had the sensation that I couldn't transmit what I wanted to the players but that is more my problem than theirs."
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Marquez's resignation came a day after Villarreal sacked Fran Escriba as coach and Alaves's Luis Zebeldia was relieved of his duties after losing the first four games of the season.
"I want to thank the president because he believed in me and I'm annoyed I couldn't return that confidence," Marquez added.
"Some people think I'm crazy but I think honesty should come first. The person who comes next will do a better job than me."
(Reporting by Richard Martin, editing by Ed Osmond)
