Speaking to ESPN Radio's "Mike and Mike in the Morning" on Thursday in New Orleans, Ware also said his team needs to play more consistently and cut back on turnovers in big games.
"We haven't been that consistent team that we need to be," Ware said. "Everybody tells us the opportunity, the gate is closing, the door is closing. The door is always closing each year because it's a business deal to have certain guys on the team."
Ware, recovering from surgery to repair a torn labrum, could need another surgery on his right elbow, according to a source.
Ware hyperextended his right elbow during the 2012 season and there was a thought rest would heal the injury. But team doctors need more examinations on Ware before a final determination can be made regarding surgery. Ware, in a separate interview on the NFL Network on Thursday, said he also played with a fractured right wrist.
"I was being a warrior out there," Ware told NFL Network.
Since breaking into the league in 2005, Ware has been to the postseason three times and has missed the playoffs the past three seasons.
Ware noted that turnovers and consistent play are the key for any team to succeed. He mentioned how consistently the Seattle Seahawks played during the season. Seattle beat the Cowboys in Week 2 of the regular season and used turnovers to take an early lead.
After the season was over, Cowboys owner/general manager Jerry Jones also talked about that Seattle game as part of the reason he fired defensive coordinator Rob Ryan after the 2012 season.
"I can say we've been underachieving at times," Ware said. "We give it what we have. But I can say we haven't been that consistent team. I wouldn't say underachieving."
Ware, however, agrees that his team is just a .500 team based on what the record has been the past two seasons.
The Cowboys finished 8-8 in 2012 and lost to the Washington Redskins 28-18 in the regular-season finale. If the Cowboys had won, they would have clinched a playoff berth and the NFC East title.
"If you play 5-5, it don't matter what the name is on the back of your jersey," he said. "You're a 5-5 team. But there's teams that will have mediocre guys, or guys that don't have quote unquote the big names but they're playing consistent and they're playing like a team, and that's what it's about."
Ware said his recovery from shoulder surgery is going fine and that he'll be ready for the start of the 2013 season. He expressed some disappointment in the firing of Ryan, whom he called one of the best coaches he ever played for, but said Monte Kiffin's new 4-3 scheme will benefit the defense in which he will move from outside linebacker to defensive end.