Off the top of my head I'd say the Rams, but I'm not 100% sure. I know both the Rams and Titans didn't make the playoffs the year before SB 34.
I was right. I just did some research because I'm a trivia geek.
Here are the only teams that won a Super Bowl with a .500 record or worse the year before:
St. Louis was 4-12 before winning SB 34
NE was 5-11 before winning SB 36
SF was 6-10 before winning SB 16
Balt was 8-8 before winning SB 35
Wash was 8-8 before winning SB 17
All the other SB winners had an above .500 record the year before winning the SB. 3 were 9-7 (Oak before SB 15, TB before SB 37, & NE before SB 38).