But the fact is, the Clippers are down 0-1 in the best-of-seven series.
And with Game 2 Monday night at Staples Center, the Clippers have the opportunity to change the course of the series in which they gave up the home-court advantage to the Warriors.
"We definitely need to win," Paul said. "When it's must-win, that means somebody has three wins. We definitely need to win."
The NBA issued a statement Sunday that said Paul was fouled by Green and should have been awarded two free throws during Game 1.
The Clippers trailed the Warriors, 107-105, when Paul was double-teamed by Steve Blake and Green out near the arc.
Paul lost the ball out of bounds with 18.9 seconds left, turning it over to the Warriors.
"Just prior to the ball going out of bounds, Paul was fouled by Green and Paul should have been granted two free throws," the NBA statement said. "Contact preceding out-of-bounds calls is not a reviewable matter."
The officials looked at the replay monitor to make sure the ball went out off Paul, awarding the ball to the Warriors.
"We still had opportunities to win," said Paul, who also mentioned that his right hamstring, which he grabbed in Game 1, was "OK." "When the ball went out of bounds, I knew it was off me. It felt like it was a foul, though."
"That was a big call. Chris Paul goes to the line now with two free throws to tie the game," Clippers Coach Doc Rivers said. "Having said that, there's nothing we can do about it. A mistake happened on their [officials'] end. But we made our own mistakes, and so we have to take ownership of that."
Rivers implied Sunday the Warriors were better prepared to handle the tense moments than the Clippers in the first game because of Golden State's playoff experience.
"They [the Warriors] played with great confidence and focus," Rivers said. "But more importantly, I thought they played with great calm and we didn't do that so well."
But the fact is the Clippers are in the playoffs for the third consecutive season and the Warriors in back-to-back seasons. The Warriors reached the conference semifinals last season; the Clippers did so in 2012.
And the Clippers' big three of Paul, Blake Griffin and DeAndre Jordan have been in intense playoff situations before and succeeded, such as winning Game 7 in Memphis in the 2012 playoffs.
The Clippers came back from a 27-point deficit in the third quarter of Game 1 in that series and 24 down with 7:55 left to win.
They were down 21 at the end of the third, trying the NBA playoff record for the largest deficit overcome at the end of three quarters.
Now the Clippers are down 0-1 to the Warriors.
"We need to win, there's no doubt about it," Rivers said. "You don't want to go down 0-2 going to Golden State, there's no doubt about that. But I really believe each game is that way. I'm not going to do anything different because it's a game that you need to win. You still have to play well. You still have to play the same."