The pair appeared emotional at a Tribeca Film Festival screening and panel discussion Thursday night as they recalled their experiences working on the black-and-white, Best Picture Oscar winner.
Spielberg said this was the first time he'd watched the movie with an audience since it was released.
At the center of the fact-based drama is Oskar Schindler, the Czech-born industrialist and Nazi Party member, who saved nearly 1,000 Jews from concentration camps by bribing officials to let them work in his factory.
Led by Neeson, Ralph Fiennes and Ben Kingsley, "Schindler's List" is a devastating depiction of how so many families were torn apart, stripped of their possessions, tortured and eventually murdered during the Holocaust.
Over the years, the director has said he hired Neeson to play Schindler, in part, because he wasn't well known to moviegoers at the time and didn't come with the kind of baggage big stars sometimes do.
"There was a lot of stuff going on. I was falling in love with my wife, who has passed away," said Neeson, 65. "Even though Steven had cast me in this, I really did feel unworthy."
He went on to say he finished the Broadway production of "Anna Christie" with Richardson on a Sunday, then headed to Poland the next day to work on "Schindler's List."
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"On Wednesday morning, incredibly early, we were at the gates of Auschwitz," the actor remembered. "Freezing cold. Trains. Guard dogs that weren't acting, of course. German actors. The whole shebang and Steven pacing up and down, very nervous. Everyone on tinder hooks."
He said his "knees were literally shaking" when it came time to film his first scene, an awful moment in which he saves a little girl from certain death by saying he needed her tiny hands to polish the inside of metal shell casings.
Spielberg, 71, recalled being stressed out at the beginning of production because, as much as he wanted to focus all of his attention on telling this important story, he still had some loose ends to tie up regarding "Jurassic Park," which would go on to become one of the biggest blockbusters of all time.
The director had to go home two or three times a week and get on a satellite feed to a special-effects studio in Northern California to approve T-Rex shots.
"It built a tremendous amount of resentment and anger that I had to do this; that I had to actually go from what you experienced to dinosaurs chasing jeeps," he said. "I was very grateful later in June, though. Until then, it was a burden. This was all I cared about."
Then he got the idea to show some of the real survivors whose characters were featured in the movie visiting Schindler's grave in Jerusalem.
"That was a desperate attempt from me to find validation from the survivors' community itself. To be able to certify that what we had done was credible," he said.
Breaking the ice
The filmmaker confessed it took him weeks to warm up to the kind and talented German actors in his movie because they were wearing Nazi uniforms and that image had such a powerful impact on him.
What finally broke the ice was when they sat down with the cast and crew for a Passover seder meal.
"The next day I talked about E.T., Raiders of the Lost Ark, Close Encounters, whatever they wanted to talk about," Spielberg said.
While those who worked on the film became a tight-knit family of artists despite their different backgrounds, the production was met by anti-semitism from the locals.
"There were swastikas that were painted at night, so when we were driving to work in the morning, we would see swastikas against walls and buildings. Just painted for us," Spielberg said.
After he completed the film, Spielberg established the USC Shoah Foundation Institute for Visual History and Education as a means of preserving the personal histories of Jews who lived through the atrocities of World War II and also in the hopes of educating future generations about what happened.
He said Thursday he believes this ugly chapter in world history should be part of the social-science/ social-studies curriculum in every public high school.
"I'm not saying my movie should, I'm saying these stories these Holocaust survivors had the courage to tell our videographers," Spielberg emphasized. "I feel blessed about a lot of things -- starting, most importantly, with my family -- but, right after that, I feel so blessed that I had the opportunity to tell this story and, 25 years later, I look at this movie tonight -- I sat through the whole film, which I haven't done in so long -- and I just was proud. Very, very proud."
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