The officials ruled Ballard was out of bounds on the play and coach Tom Coughlin challenged during the Giants' 38-35 loss to the undefeated Packers on Sunday.
Referee Jeff Triplette reviewed the play and upheld the call on the field.
Asked about losing two challenges in the game, Coughlin said Monday he felt sick about the first one because he had just seen a still photo of the play and Ballard had one knee down in the end zone, making it a touchdown.
NFL spokesman Greg Aiello said officials don't look at still photos when they review a play.
With the score tied 7-7, Coughlin said the original call on Ballard's catch was too close not to challenge. He lost the review, but said looking at the still photo on Monday made the decision feel worse.
"I just saw a picture which made me sick to my stomach, which Fox produced and showed, that he's in," Coughlin said. "Don't ask me about that because I really don't know why, but I did see the picture."
New York settled for Lawrence Tynes' field goal after the ruling on the field was upheld,
Coughlin also challenged a 7-yard, third-down reception by Donald Driver early in the third quarter on a third-and-3 from the Giants 40 and lost that one, too.
"I really shouldn't have challenged," Coughlin said. "It was right on our sideline, but it was a third-and-3 and I was very much aware of where the ball was going, where it was headed, and if there was any way that [it] could have been turned around and they were hurrying up to the ball to snap it. So I really didn't get a great call from upstairs."