Jones fired the first shot at a pep rally-type ceremony at the start of the Cowboys' training camp, telling fans in Oxnard, Calif., that they should travel to "watch us beat the New York Giants' ass."
Giants linebacker Mathias Kiwanuka responded on WFAN radio in New York last week, saying Jones should be motivated because the Giants "have been whupping his ass for a long time." Kiwanuka added that it "must be tough to be on the outside looking in at all these championships lately."
To that, Jones has no retort as the Cowboys prepare to travel to MetLife Stadium for Wednesday's NFL season opener.
"It just reminds me that he's right," Jones said Tuesday on KRLD-FM. "They have taken the bacon from us the last few years and certainly last year.
"They played the regular season at 9-7. We do know that given a couple of completions, we could have been in those same shoes. I don't know of anybody that was playing better than the Giants at the end of the year. So there is no doubt that we can, we could, we should have been focused on this opener and playing the New York Giants. I don't back away from that emphasis at all."
The Giants have won seven of the last nine meetings with the NFC East rival Cowboys. That includes a couple of elimination games en route to the Giants' two Super Bowl titles in that span.
New York knocked off the top-seeded Cowboys at Texas Stadium in the 2007 divisional round en route to the Super Bowl XLII title. The Giants punched their playoff ticket and made their Super Bowl XLVI run possible with a 31-14 win with the NFC East title at stake in last year's regular-season finale, ending what Jones has called the most disappointing season for Dallas in his 23 years as owner.