Half of the Giants accepted praise and quickly determined that their bold step forward must not be a temporary development.

That would be the defense.

The other half realized they were fortunate that their failings did not result in another loss.

That would be the offense.

The Giants gained their first victory of the season by beating the Redskins 20-14 and now move on as an honest-to-goodness favorite to Sunday’s home game against the battered Browns. Even with the incredible seven turnovers they forced, the Giants barely were able to protect a 20-7 lead, as their offense managed just four first downs and scored no points in the second half.

There’s no doubt a strong sense of relief filled the air as the Giants ended a nine-game losing streak and won for the first time for coach Tom Coughlin after opening the season with a 31-17 loss in Philadelphia. Just as pervasive, though, was a sense that forcing more than half-a-dozen turnovers is a once-a-season happening and that given that rare occurrence, the verdict should not have been in doubt.

“We didn’t do enough of the good things when we had the chance,” left tackle Luke Petitgout said. “Our defense came through, any time the other team has seven turnovers the score shouldn’t even be close, unless you have six, and our offense didn’t have any. We got to score more points. But it’s a little easier to stomach some of the things after a win than after a loss.”

No doubt. Coughlin stated, “It’s a better platform to teach from when you win,” and the taste of success was badly needed, considering all the early-season negativity swirling around the team.

“It’s not so much a relief, it just feels good,” cornerback Will Allen said. “That’s the end of that. Giants haven’t won, dah, dah, dah, that’s the end of that. Now let’s start something new, let’s start a new streak.”

To do so, the running game can’t average a mere 2.2 yards per carry and the offense cannot lean on the defense to set up every point for it. Coughlin maintains he did not deliberately close down the attack in the second half and play conservatively. With bad field position, though, the priority was holding on to the ball and the Giants did do that.

“I asked myself this one when I looked at the tape,” Coughlin said. “Obviously that’s not the way you want to play a half or a quarter or a football game. What really has to be said about the second half offensively was there were things out there we left on the field.”

And finally, Kurt Warner broke through with his first touchdown pass (he had none in the preseason or in the opener) on a 38-yard rainbow to Tim Carter and Coughlin assessed his quarterback as “very solid.”

Warner wants more.

“I keep thinking gosh, I have so much more, I can play so much better than I did the first two games,” he said.

There were no such qualifiers by members of the Giants defense, who hope to duplicate their showing against the Skins, as improving on the mayhem they created will be difficult.

“It’s been a while since we’ve had fun here,” said linebacker Barrett Green, who scored his first career touchdown on a 16-yard fumble return. “We’ve been working so hard to do things right around here, it felt good to let it loose and have fun. It was good to come out and make some plays in front of our home crowd. Kind of let the New York fans know what we can do as a defense.”