The Giants saw the ball turned over six times on their way to a 36-31 defeat at the hands of the Dallas Cowboys, including an interception touchdown with under two minutes left on the clock that ultimately proved to be the deciding play.
"You are not going to win the game turning the ball over five times and muffing a punt," Coughlin told The AP.
"I'm totally, totally disappointed, embarrassed about that football. That's sloppy, sloppy football."
The Giants will have another chance to pick up their first win of the new season when they take on the Denver Broncos on Sunday.