Jones said: "It was a tight game and we made the mistake that has cost us. We will be hung, drawn and quartered now for a week but it's only one game and there is still a long way to go.
"We had good chances but there was hardly anything in it, only half-chances for both clubs and their goal came because our defender was too tight.
"We have allowed the gap at the top to close. That is all. We needed height down the middle and I had to make decisions but now we will have to lick our wounds and get on with it.
"We had a couple of good chances but it was a fine line and that is how derby games are.
"We were a little below par and one bad defending decision and lack of concentration has cost us, but there was never much in the game."
Swansea boss Brendan Rodgers is hoping the hard-fought win will throw his side into the spotlight.
The Swans are now just three points behind second-placed Cardiff and a further point behind leaders QPR.
Rodgers said: "It was a fantastic result and a wonderful team performance because to come to Cardiff and win such an emotional derby game is superb, both for the players and our fans.
"Cardiff gave us massive respect by changing their style to 4-3-3, so it took us time to settle down.
"When the game is tight, we have the players who can take it on in the second half and our idea of the game was to dominate by playing football.
"We have youth and experience and we were inventive so the players will enjoy this evening but the job starts again tomorrow.
"We are playing with confidence. It has been a successful day but we now go on to Wednesday's game.
"We don't get a lot of coverage so it was good for the nation to see how we play and I'm very happy for the players and supporters.
"Our starting XI is as strong as the top two teams in this division but you won't hear any talk from us about promotion.
"We have shown great consistency and as long as we keep on progressing then I will be satisfied."