The game, played in suburban New Jersey, went ahead as planned despite the devastation of Hurricane Sandy.
The Giants had won their four previous outings, however Coughlin said: "We wanted emotionally so badly to win the game for all our neighbours who are struggling and who need some type of inspiration.
"What we were trying to do was to give them a few hours of enjoyment in a very difficult time, to let them know that we understood the mass difficulties facing our neighbours and that many people are fighting to survive, fighting to get their homes back, to get their families reunited in the aftermath of a tragic storm. We were trying but we didn't accomplish what we set out to do."
The Giants had looked a good bet for a fifth successive win, though, as they led 20-10 going into the final quarter.
Andre Brown's one-yard touchdown run and Michael Boley's 70-yard return from a Ben Roethlisberger fumble - coupled with two field goals from Lawrence Tynes - had put the Giants in charge.
Roethlisberger had earlier connected with Emmanuel Sanders for four-yard touchdown pass, while Shaun Suisham kicked a 30-yard field goal to keep the Steelers in touch.
However the visitors came alive in the final quarter with Roethlisberger, who completed 21-of-30 for 216 yards, throwing a 51-yard touchdown pass to Mike Wallace.
And then with four minutes left, Isaac Redman scored the winning touchdown from a one-yard run.