Kiffin's defense allowed Chicago to score on eight straight possessions. Backup quarterback Josh McCown threw for four touchdowns, and the Bears were 8-of-11 on third-down attempts.
"He takes it personally; it's hard on him," Jones said of Kiffin during his twice weekly radio show on 105.3 The Fan in Dallas. "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."
After the loss, Jones said he wished the Cowboys (7-6) would trick up some of their defensive schemes and get more pressure on the quarterback to create turnovers.
When told of Jones' comments, Kiffin told ESPNDallas.com: "We blitzed early, you know, and tried to get some pressure and they got the ball off, and we mixed it pretty well."
The Cowboys used a mixture of man and zone coverages, but the secondary struggled to make plays. Chicago had five pass plays of 20 or more yards.
"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," Jones said. "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 have allowed 24.9 first downs per game this season, which is on pace to be the worst by any defense since the 1981 Baltimore Colts (25.4).