McAtamney had missed three extra point attempts in the past two weeks.
"Got to make the kicks," said McAtamney following the loss. "Not gonna shy away from that. I'll take full responsibility."
He was part of a pair of signings after the Giants' starting kicker Graham Gano was out with a groin injury, the other kicker was recently released Atlanta Falcons kicker Younghoe Koo.
McAtamney initially won the competition over Koo, but now Koo will remain on the Giants' practice squad while Gano is set to make his return.
The 25-year-old Derry, Ireland, native McAtamney now leaves the Giants after going 9-for-12 in extra points and 1-for-1 in field goals.
