"He should, he should," Kiwanuka said on WFAN radio Thursday morning. "The New York Giants have been whupping his ass for a long time. I mean it has got to be tough on the outside looking in on all these championships lately.
"But that is the feeling I feel like everybody in the league has, and what they should have," Kiwanuka continued. "Because when you are on top, everybody should be wanting to knock you off."
The Cowboys will get the first crack at the defending Super Bowl champions next Wednesday when the Giants open their title defense against Dallas at home to kick off the NFL season.
Kiwanuka was responding to Jones' comment earlier in training camp when the owner implored Dallas fans to come to Cowboys Stadium later in the season.
"Y'all should come to that (Cowboys) stadium and watch us beat the New York Giants' ass," Jones said at a ceremony signaling the start of Cowboys camp back in late July.
The Giants swept the Cowboys last year to win the NFC East and went on to win the Super Bowl. The Giants barely responded early in camp after initially hearing Jones' comment.
Defensive captain Justin Tuck said he had no problem with Kiwanuka's response.
"Why not?" Tuck asked. "I don't see why everybody else can talk about us and we can't fire back. So I ain't got no problem with it."
When the Giants first heard Jones' comment back at the start of training camp, several players just smiled and laughed it off.
"I am still laughing it off," Tuck said. "Kiwi is a confrontational guy so I am not surprised by [his reaction]. [But] we are not a team that looks for bulletin board material. Our energy and our attitude going forward to our next game is going to be great regardless of whether we got a team singing our praise or telling us we [stink]."