Interviewed separately as they came out of the Giants locker room, both players said they were "good," although Ware added that it was as much as he could say about his condition.
Ross was injured on a scramble to intercept a tipped ball that also sent defensive end Jason Pierre-Paul to the ground, but Pierre-Paul soon returned.
"Fortunately, JPP was able to get up and go and I just saw Aaron Ross and he just counted fingers for me so I hope he's all right," Giants coach Tom Coughlin said after the game.
The Giants were up 10-2 at the time.
"It was all of us, Justin Tuck, me and Aaron," Pierre-Paul said, "and they hit me on the side and I got the wind knocked out of me. But after that I was fine."
As he was down on the field, the MetLife Stadium crowd started to chant, "JPP!"
Defensive end Osi Umenyiora said he knew Pierre-Paul was fine.
"He was trying to milk it a little bit," Umenyiora said. "He lay down, the crowd gave him the little JPP chant and he got (up) like he was Optimus Prime or something."
Rookie Prince Amukamara took Ross' spot. At the time Ware went out, he had a carry for four yards and a catch for 13 yards. It wasn't clear how he was injured.
Falcons safety William Moore suffered a groin injury in the first half and didn't return. With Moore hurt, the Falcons were without two of their four starters in the secondary. Cornerback Brent Grimes was inactive for the game with a knee injury.
Giants safety Deon Grant sustained a quad injury in the first half but returned for the third quarter.
Grant said in the locker room after the game that he planned to be ready to play in Green Bay when the Giants face the Packers on Sunday afternoon.
"This is a physical sport," he said. "Football is a physical sport so I'm expecting pain -- I don't care anything about it."
Jake Ballard, who suffered a partially torn posterior cruciate ligament in Week 15, had two catches for 16 yards.
"I felt all right," Ballard said. "Not 100 percent, but better than I did last week, so it was just kind of a confidence booster."
The NFL recently decided to pay for an independent trainer to be on site at all games to determine whether players with apparent head injuries can return to a game.
Meanwhile, Giants linebacker Mark Herzlich, who missed Sunday's game and has not played since injuring his ankle on Nov. 28 in New Orleans, updated his status for next week's game in Green Bay via Twitter.
"Trying with everything i have to be ready for next week!! Test it again on Tuesday," Herzlich tweeted.
Jane McManus is a columnist and reporter for ESPNNewYork.com. Information from ESPNNewYork.com contributor Mike Mazzeo and The Associated Press was used in this report.