"Every week there was something new," Travolta, 61, exclusively told PEOPLE during the FX Winter Television Critics Association Press Tour on Saturday in Pasadena, California. "For me, it was the legal system and the judicial system. I didn't realize how they were so designed for themselves and not really for the humanities for for fairness, but how clever can you be to work the system. That was interesting to me as an overall thing. And also the antics and the egocentric things that were happening between the lawyers was very interesting insight."
The 10-part miniseries, directed by Ryan Murphy, will serve as Travolta's first reoccurring appearance on a television show since his days on Welcome Back, Kotter. Though the part seemed demanding, Travolta was ready to give it his all.
"So when I was offered this challenging role and investigated the reasons why I should do it or shouldn't do it – and found out it was not going to be a guilty pleasure, but instead something meaningful ... I decided to tackle it with a full court press, if you will, and really try to give as much reality of Robert Shapiro as needed," Travolta told reporters.
Though Travolta chose not to meet with Shapiro in person, he said they corresponded.
"I got a letter from Shapiro telling me that he was happy that I was playing him," Travolta said. "Once you feel like you've got what you're going to do, meeting the real-life can be helpful or maybe take you in a direction you didn't expect. So, it's tricky."
There's no doubt that the Pulp Fiction alum has had his share of special projects, but this one in particular was different ... in a good way.
"I've never worked on a project where I felt more of a team effort to make something happen naturally, effortlessly," Travolta said.
That being said, the topic of Fox's Grease Live did come up.
"It was such an iconic thing for me, Grease," the actor said. "They do it in summer theater, they do remakes on Broadway, they do off-Broadway and they do high school and college productions so it's a very done thing. The idea that they're doing a live production on television isn't that different. It's just being televised. ... Now that I know when it is, I might tune in. Why not?!"
Can we expect any live musical cameos from Travolta?
"Probably not in the live aspects," he said. "I did 16 years of theater and you know, my cup runneth over in the live productions, but a musical movie? Yes."
American Crime Story: The People vs. O.J. Simpson premieres Feb. 2 at 10 p.m. ET on FX.