The actor – who played Robert Todd Lincoln in the movie – praised Day-Lewis and director Steven Spielberg's approach to shooting the Abraham Lincoln biopic.
"The whole set revolved around [Day-Lewis], and as it should have," Flicks and Bits quotes Gordon-Levitt as saying. "I think that really speaks high to Steven, because a less experienced and perhaps more egotistical director [might not have]."
He continued: "Generally the set revolves around the director, but on Lincoln Steven really centred everything on Daniel, the President – he called him Mr President. I think that was key and for me it made it just so I could slip into the world."
Gordon-Levitt went on to further praise Spielberg for creating an enjoyable atmosphere on the Lincoln set.
"What I noticed the most about Steven immediately that stuck with me was just how happy he was to be on set, and how enthusiastic and gleeful he was," the star recalled. "You know, you'd think, 'Steven Spielberg, he's one of the most successful and renowned filmmakers of all time, probably it's just another day at the office for him'.
"But not at all! I think this project was really special to him. This was a particular movie that he's been trying to make happen for years. Just every day, every shot, he had just such love for what he was doing. And that's contagious."
Gordon-Levitt previously revealed that Abraham Lincoln is portrayed as a flawed man in Spielberg's movie, rather than an entirely selfless hero.
Lincoln - which is adapted from Doris Kearns Goodwin's book Team of Rivals - is released on November 16 in the US and January 25 in the UK.
Watch a trailer for Lincoln below: