Woodley joined from the Pittsburgh Steelers this off-season, moving to the Raiders alongside league veterans Justin Tuck, Maurice Jones-Drew and Matt Schaub as the franchise aims to qualify for the post-season for the first time since 2002.
He told KGMZ-FM: "I can definitely see us as a playoff team. Last year going back and watching some film on the Raiders, there were a lot of opportunities here where they just didn't close it out.
"Some games good in the first half, they just didn't close it out at the end of the game. So now we just have to learn how to close out games and it'll be more wins than losses.
"Us veterans didn't come here just because, oh, we are just trying to get a few more years in in the NFL. No, we've come here to win and help play a role to take this team further."
The Raiders finished the 2013 season with a 4-12 record, losing eight of their final 10 matches following their bye week.