Kiffin has come under criticism this season due to the Cowboys' poor defensive record, an issue that was highlighted once again on Monday night when the Chicago Bears made almost 500 yards and scored on eight straight possessions on their way to a 45-28 victory.
Jones acknowledged that there is a problem that needs sorting in the defence, but is confident that the 73-year-old Kiffin is the right man to solve it.
"He takes it personally; it's hard on him. Very hard on him. He's been doing this a long time. At his age, he's had a lot of different experiences. With all of that in mind, he's just got a resolve and he doesn't in any way reject the responsibility. As a matter of fact, he invites it all on himself," Jones told 105.3 The Fan.
"To be doing what we're doing and to fix what we're doing, there's nobody I would rather have than him and [defensive line coach] Rod Marinelli. Where we are today, to get this fixed over the next, if you would, week or four or five days, the next three weeks, there's nobody I would rather have to get it fixed.
"First of all, he knows what's happening to us better than anyone. And if there are adjustments to be made, he's the right man for the job right now."
The Cowboys are currently second in the NFC East, one win behind leaders the Philadelphia Eagles with just three games left to play.