Palace co-chairman Steve Parish announced the news at a hastily-arranged press conference.
The defeat to Fulham left Palace second bottom of the Premier League, with seven losses from eight games.
Parish said: "Ian's contract at Crystal Palace has come to an end by mutual consent.
"Ian felt that a new approach might help keep us in the division.
"I've enjoyed every minute of working with Ian. He leaves our club with his head held very high.
"I'd like to put the record straight. We've never fallen out. We've worked together brilliantly. We feel we need to move on to progress."
Holloway only took over at Selhurst Park last November and led them to promotion via the play-offs.
But this season only Sunderland's woeful form has kept them off the foot of the table and the thrashing at home by fellow strugglers Fulham was the final straw.
Holloway said: "I have pride in the job we've both done. It wasn't easy. If Steve's last manager (Dougie Freedman, who left for Bolton) wasn't headhunted I wouldn't have been here.
"We need to shut up shop in this division. At the minute we've got a whole new group there.
"Part of my talking with Steve was about am I the one with the energy left?
"I have to hold my hand up and say we didn't keep the spirit that got us up. We changed too much too quickly."
Holloway was brutally honest in his assessment of the situation, saying the club has "lost the spirit" they had last season because of the raft of new signings.
Palace signed enough players for an entire new team over the summer, bringing in the likes of the much-maligned Marouane Chamakh from Arsenal, Reading pair Adrian Mariappa and Jimmy Kebe, Jerome Thomas from West Brom, Jose Campana from Sevilla, Stephen Dobbie from Brighton, Dwight Gayle from Peterborough, Elliot Grandin from Holloway's former club Blackpool and, on loan, Southampton's Jason Puncheon and Stoke's Cameron Jerome
Holloway said: "I hold myself and Steve responsible. I didn't value enough the spirit of the group that helped us get to the Premier League
"I've lost the spirit of that group. I owe it to the lads to admit that.
"I'm not saying my new signings aren't good enough. But they need to buy into this football club the same way my other lads did.
"It is a privilege to have worked at Palace. With me out the way, the new man will have a chance to start again.
"I could never work any harder than I have done."
Parish said he would consult Holloway when it came to appointing the new manager, saying they needed someone with more top-flight experience.
"We've got a whole group of people who are only really used to the Championship and dropped them into the Premier League," he said.
"I think we both realised we need someone with more experience at this level."
Parish emphasised that he never had any intention of sacking Holloway, praising the 50-year-old for doing the "honourable thing" and admitting he was not the man for the job.
He confirmed Keith Millen would take temporary charge for the match against Arsenal on Saturday and he had no permanent replacement lined up.
Parish said: "I was more than happy to get relegated and come back up with Ian. The word 'sacked' has never been mentioned among the directors
"Ian's been very noble and he's come forward and said, 'I can't do it'.
"Ian feels very strongly that we need to stay in this division. It's so difficult to get out of the Championship now.
"You'd love to have someone in place next week, but I haven't got a list. I wanted Ian to wake up and say 'sorry about the blip' and stay."
Holloway added: "This club needs an impetus of energy. But I just feel tired to be honest. I'm worn out.
"All I can do is be as honest as I can and wish everyone at the club well. I just need time to chill out."