Preston and Burnley kept their nerve to win and dump City out of the play off places on the final day.
"It's probably my biggest disappointment." said Jones. "Relegation at Wolves was a hard one to take, but when you're so close and you've been close for a long time - 45 games we've been close - to lose at the death is a gut-wrencher.
"We have to learn from it. It's harsh lesson to learn. We'll pick ourselves up, dust ourselves down and get ready again."
Cardiff blew an 8 point lead and a massive goal difference with the side just not being able to handle their position.
"It's that mental side of the game and a lot of these players have not been in this situation before," added Jones.
"It's a horrible feeling. I missed out at Wolves one season in the play-offs and we were stronger for it.
"That's what this lot, the ones that stay, have to be. Some are going to get hammered from all quarters and they've got to take it on the chin and we've got to be strong for it.
"They're so disappointed it's hard to take in, but the only way of getting rid of it is by going again next year.
"Ability-wise, running, strength, pace, it's all there, but maybe we just lacked that mental strength to see it through."
"I thought the team was good enough. It proved it wasn't. We'll all look at ourselves, but I thought this squad was good enough to go up, not in the play-offs but automatically.
"But the table doesn't lie. We had a fantastic record until four games ago and we'll all take responsibility."
Winning manager Brian Laws said "You've got to give credit to my players. Their attitude has been first class and even though we've been secure for a few weeks, they've never switched off.
"They've given everything they can and all you can ask is for them is to be honest, give your all and be honest to the other teams in the league.
"It's about 46 games, not 45 or 44, you've got to finish the job off in a professional manner.
"I'm gutted for Dave, particularly because he's a good guy. He'll be very disappointed, but I'm sure he'll reflect over the 46 games and not just this one."