HEMPSTEAD, N.Y. - Brett Favre has watched film of his ill-fated throw in the NFC championship game and replayed it in his mind countless times.

There was no way, many thought, the three-time MVP could step away from the game with that as the last image of his storied career. Redemption, despite all the records and victories, had to be the reason Favre stepped out of retirement, right?

“I can see where people would think that,” the New York Jets quarterback said Tuesday. “That’s happened to me twice in my career and believe me, it’s disappointing, but wanting to come back for one play, to me, is obviously the wrong reason to come back. Or wanting to come back to prove someone wrong, or wanting to come back from what happened this offseason.

“The only reason I came back was I wanted to play. It’s as simple as that.”

But what if the Packers had beaten the New York Giants to go to the Super Bowl?

“Maybe we’re not here,” he said. “I have no idea.”

Favre struggled in subzero temperatures in Green Bay on Jan. 20 and his wayward pass to Donald Driver in overtime was intercepted by Corey Webster. The pick set up Lawrence Tynes’ winning 47-yard field goal in the Giants’ 23-20 victory.

“Believe me, I wanted to win the game, but I give them a tremendous amount of credit and respect,” Favre said. “That’s over and done with. Obviously, it’s a new year and a lot of things have changed.”

That’s for sure. Starting with the fact that Favre is now on the Jets, who take on the Giants on Saturday at the Meadowlands.

“It’s a preseason game for us,” he said. “I’m not thinking about the past. They’re the team to beat in this league and we’re just trying to get better this week.”

Favre was pretty good in his debut with the Jets, going 5-of-6 for 48 yards, including a 4-yard touchdown pass to rookie Dustin Keller. Jets coach Eric Mangini said he was uncertain how long Favre will play against the Giants, but the projected starters usually play a large chunk of teams’ third preseason games.

“With every preseason game I’ve played in, I’d like to play the whole game,” Favre said. “If I’m going to come out here and practice, I want to play the whole game. That’s just my mentality. Will that happen? No. We’re going to be smart about it and whatever Eric wants to do, we haven’t really talked about it.”

Since coming to the Jets following a bitter divorce with Green Bay on Aug. 6, Favre talked about how his biggest hurdle has been getting the terminology from a new offensive system down. After 16 years with one team, it’s not something Favre can easily handle on the fly — the way he has done so many times on the field.

“For the most part, it’s the things that people don’t see that we’ve got to get on board with in a hurry,” Favre said. “Sight adjustments, audibles, things like that. What’s the easiest way for me to get to those? Is it using a term that’s already in place, or maybe coming up with a new term? And not to mention changing it up and having more than one term for a lot of things. I mean, it’s a work in progress and I think that’ll be the case all year long.”

Favre said he and his receivers are working at getting on the same page on the field, and some of the quarterback’s signal-calling suggestions were in place during practice Tuesday.

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“In our 2-minute drill today, we made some real good plays, a lot of signals were given today, some things that I had recommended maybe we try,” he said. “We kind of just turned it loose today. We did good on a couple and didn’t do quite as well on the other ones. The good thing is that it was practice. We can go back and look at it on film and make the corrections.”

One of the mistakes came on a pass intended for Brad Smith that was intercepted by Darrelle Revis.

“I think we’re making strides,” he said. “To me, it gets worse before it gets better.”

Favre and Mangini have spoken every day about what the quarterback’s needs are.

“Our communication has been great,” Favre said. “I said, ’Well, there’s no substitute for game-type situations.’ The 2-minute drills, red-zone situations, third-down situations, you can’t do them all in one day, but we’re trying to throw those in.”

Favre has often described his new career with the Jets as “different” and a scenario he never would’ve dreamed of. He was asked what his father, Irvin, who passed away in 2003, would’ve thought of all this.

“He was pretty straightforward,” Favre said. “He would’ve wanted me to play all along, and I’m sure it would’ve been in Green Bay. But he’d probably be out here at practice every day raising hell with me, what I could be doing better. He would’ve wanted me to play until my legs fell off. That’s just the way he was.”