Holloway quit his post at Selhurst Park on Wednesday, admitting he was too 'tired' to become caught up in another Premier League relegation battle.
Holloway leaves the Eagles after just under a year in charge and having guided the club back to the top flight via the Championship play-offs.
He has however been unable to make Palace competitive among the elite - Palace have picked up just three points from eight outings so far.
Holloway told Sky Sports News: "I've had a whirlwind year here and they are fantastic people. The club has achieved so much, I'm proud of that part, and I hope it goes on to achieve what no other Palace side has done and stays up.
"The results aren't right at the moment so I have just told them to gel as a group, gel for the new person, whoever it is, and I'm sure the luck will change."
He added: "You've got to take the emotion out of it. It's difficult. Football is what it is and if you're at the bottom of the Premier League, the pressure is on the board to do something.
"They have just got to realise that they haven't been that far off getting a half-decent result, and once they get one then that will build, that will gel and will get there.
"What I should have done is reward more of the squad who were with me and not try to change too quickly, too fast. Steve (Parish) knows part of that is him as well as me, but I wish him all the very best now."
Asked if he has any regrets, as a second spell as a Premier League manager comes to a close, the former Blackpool boss said: "There always is, but this club is bigger than me. This club's bigger than anybody and the fans deserve a fresh start and a fresh chance. Good luck to them."