Holloway and Palace co-chairman Steve Parish announced the split by mutual consent at a hastily-arranged press conference, which came two days after the team lost 4-1 at home to Fulham.
The former Blackpool boss said he did not have the energy for the relegation fight, claiming the club had lost the spirit which helped them win promotion to the Barclays Premier League last season because of their raft of summer signings.
The defeat to Fulham left them second bottom of the table, with seven losses from eight games.
Holloway said: "This club needs an impetus of energy. But I just feel tired to be honest. I'm worn out.
"I want to give them the chance to stay in this division.
"They didn't want me to do this. They've got a great chance, they've got 30 more games. The best chance they've got is if they use some of the money this big division gives them to get someone they couldn't afford when they chose me, and if that happens, sitting at home in my front room, no one is going to jump higher than me."
Parish added: "He felt things weren't working for him, he felt that he wasn't getting the support that he wanted to get and a different approach might keep us in the division."
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.
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 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."
Parish said Holloway had run himself into the ground doing his own scouting over the summer.
"We came up very much as a Championship club," he said. "The amount of work that went on in the summer was extraordinary, Ian was watching player after player. We should have had more of a scouting infrastructure in place."
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 said: "He leaves our club with his head held very high.
"He's a remarkable man, he's done something that most people wouldn't do, and said, 'we need to talk about the situation, I don't think it's working at the moment'."
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 he would consult Holloway when it came to appointing the new manager, saying they needed someone with more top-flight experience.
Former Stoke boss Tony Pulis would fit that bill, having established the Potters in the top flight before leaving at the end of last season.
On Pulis, Parish said "He's never been relegated, and he's out of work. We'll look. People with some kind of affinity with the club, that does help when times are tough. I wouldn't discount anyone."