"We started well and brightly, but giving away the penalty was a piece of stupidity," said Jones.
"It was a horrible mistake and stupidity costs you.
"After they went down to 10 men we conceded, which made it an uphill struggle.
"We basically just did not deal with a free-kick.
"We kept the pressure on, but when we went and did what we did for the last one, well, that was the killer.
"There was a lot of stupidity and a lot of my players have to take a long, hard look at themselves. Too many of my players did not show enough commitment. Now we need to dig deep."
Meanwhile Daren Ferguson was full of praise for man mountain Jon Parkin. The lumpy striker scored twice as Preston rolled City over.
"Jon took Cardiff to the cleaners and absolutely battered them," said the Preston boss.
"The second and third goals, I don't think you'll see better goals all day.
"John is a big lad, size-wise, but technically he's as good as anyone.
"He's been spot on and has taken his chance. All credit should go to John.
"But it was a great afternoon for us; three goals and a clean sheet, so the lads deserve a hell of a lot of credit."