Jones' side needed a point to guarantee themselves a top-six finish, but a "gut-wrenching" 1-0 defeat at Sheffield Wednesday, coupled with Preston's 2-1 home win over QPR, ensured the Bluebirds' season ended in heartbreak.
Jones said: "It's probably my biggest disappointment. 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."
Wednesday winger Jermaine Johnson slammed home a spectacular volley from the edge of the penalty area in the 70th minute to condemn Cardiff to another season in the second tier by the narrowest of margins.
Both Cardiff and Preston finished level on 74 points with an identical goal difference, but the Lancashire side snatched the last play-off spot by virtue of having scored one more goal than the Welshmen.
Jones' side have taken just one point from the last 12 on offer, conceding a dozen goals in the process, and will look back on their shocking 6-0 defeat to Preston at Deepdale last month as the day a campaign that had promised so much began to unravel.
Jones said: "It's that mental side of the game and a lot of these players have not been in this situation before.
"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."
Jones added: "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."
Wednesday manager Brian Laws paid tribute to his players' attitude during the run-in and spared a thought for his opposite number.
The Owls closed the season on a high with an 11th league win at Hillsborough.
Laws' side needed to beat Norwich at Hillsborough in their final match last season to guarantee their survival, but have played with a freedom in recent weeks having assured themselves of a mid-table finish.
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."
Laws confirmed he would be strengthening several key positions with some experienced players in the summer in the hope of launching a play-off push next season.
He added: "Why not? You've got to set your targets as high as you can, but with realism, or players won't buy into it otherwise."