The redshirt freshman from Pace figured his playing time at Florida State would be relegated to mop-up duty.
Norris has played in key situations for the Seminoles this season, including 18 snaps in last Saturday's win at Wake Forest.
Moore returning from an ankle injury, Norris might have a reduced role in Saturday's game against Maryland.
But that's fine, too.
"I feel like I am playing better than most people thought I was," Norris said and laughed.
"I thought I would get into the game and freak out and be nervous. But the first play was kind of nerve wracking, but after that everything was fine. It has been fun.
"I felt like going into the year, I'd be mop-up crew. I think it's just (a matter of) working hard and focusing in on assignments that have made coaches confident I can play.''
Norris said one key to his success has been his ability to retain his strength and weight. He's still around 255 pounds.
Norris, who has played in the past four games after making his first-career appearance against Alabama-Birmingham in the season's second game, believes another key has been the ability to learn behind experience players like Moore.
Overall, FSU's defense has proven to be one of the country's best, especially against the rush.
"We have so many good players," Norris said. "All of our starters are good, great players.
"Plus, you have real good players behind them as well. I feel that makes us good. You can pull people in and out and keeps everyone fresh and everyone plays with the same intensity. I feel good."
Zook was fired on Monday, though he will coach UF through the remainder of the season.
"One of my good friends is a Florida fan and he was telling me that he (Zook) had to win out or he was probably going to get fired," Norris said.
"But I didn't think they would fire him during the season. That was a big surprise."