According to the 50-year-old actor, when they first started their film about a tank unit invading Nazi Germany, they talked about how great it would be if they could do it and bring it back to the soldiers.
The also had already been through months of training by some of the best military figures.
"We'd had many conversations with vets who were there and we got a much deeper understanding of what these men and women endure and give of themselves to keep us in our comfy homes and driving our cars," Pitt told the Ledger-Enquirer.
"So for us it's a very special day, and I hope we got a few things right for 'em -- that'll be our ultimate review," he added.
Before the special screening, "Fury" director David Ayer Pitt, his co-actors Shia LaBeouf, Logan Lerman and other cast members met with the soldiers.
Pitt said Brees is still one of the best quarterbacks in the world.
Not only is the actor a huge fan of New Orleans Saints; he is also friends with the former Super Bowl champ.
Earlier this year, Angelina Jolie's husband was spotted throwing a football with the New Orleans Saints quarterback and "Dallas Buyers Club" star Matthew McConaughey from the balconies of their Bourbon Street pads.
Meanwhile, Brees commented on Reggie Bush being drafted by his team.
"I think it was significant. I'm not sure if there has been a player where there was as much hype and excitement for coming out in the draft as Reggie Bush. Maybe you could argue Johnny Football (Manziel) this year, but he was the man," he told New Orleans Saints.
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