"Don't make mistakes. They've got a chance to be as good as anybody," Bowden said.
The Seminoles defense flexed its muscles in last Saturday's home-opening victory over Alabama-Birmingham.
FSU limited UAB to 144 total yards for an average of 2.9 yards per play.
The Blazers were just 3 of 14 on third-down conversions and had just seven first downs by either rushing or passing. They finished with 11 first downs overall, thanks in large part to FSU penalties.
In addition, the Seminoles finished with eight sacks.
"When I saw Miami and Florida State play, I said that might be the two best defenses in the country playing in the first game of the season," UAB coach Watson Brown said.
"I don't believe I have played a better defensive football team since I have been here than that one."
Sims was pleased to help the Seminoles rebound from their season-opening defeat at Miami.
"Basically, UAB isn't really the big powerhouse schools, so we wanted to stay focus and we didn't want to let up," Sims said.
"As far as that went, we did well. It was a good, positive step but we did have some letdowns. That's something we have to work on."
Safety Pat Watkins, who snagged his second interception of the season, agreed.
"We just wanted to start where we left off the Miami game," Watkins said. "We didn't finish but we know we dominated as far as the game went. This time we weren't going to let up and play all of 60 minutes and show we are one of the best defenses in the country."