"They were flying after a great result last week but we showed our teeth.
"Chris Burke has done superbly, he played all of the game and extra-time in midweek and then he's come and put a shift in. That's what he's like, he's a little firecracker and I thought that all the midfield were great. Some of the football in the second half was outstanding."
Cardiff defender Kevin McNaughton was stretchered off with a neck injury which held up the game for nine minutes near the end of the first half and Jones said: "He's gone off to hospital and we are just waiting to see how he is. It was an accidental injury, he caught someone's knee and we are having him looked at as a precaution."
Derby manager Nigel Clough admitted his side were not at their best.
He said: "It was a funny sort of game really.
"It was heading to 1-1 which would have been a fair result, but one mistake has cost us.
"We didn't get a break in the six-yard box, they got one break in there and we didn't.
"Cardiff are a settled side who have been together for three seasons and you can see that but still we have come close to getting a point against them.
"For their second goal, Gareth (Roberts) should have cleared it and Stephen (Bywater) should have saved it.
"The first goal came after Kris Commons gave it away in our half and they broke. He (Michael Chopra) has done two of the lads and it was too easy really. We can't afford to give possession away where we did.
"The young lads are learning but they have got to learn more quickly than that.
"They are all disappointed because we know that we can play better than that and we will do. These are the sort of games where you make sure you don't lose and you come off with a point, and that's the mentality we are trying to instil."