"I can definitely see [the Raiders] as a playoff team," Woodley said Tuesday during a radio interview with 95.7 The Game. "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."
The Raiders went 4-12 in 2013, their 11th consecutive season without a winning record. Oakland has not reached the postseason since appearing in Super Bowl XXXVII after the 2002 season.
But the Raiders were aggressive in free agency this offseason, adding a bevy of former Pro Bowlers, including Woodley, Justin Tuck, Maurice Jones-Drew and Carlos Rogers. Oakland also signed former Green Bay Packers wide receiver James Jones and acquired veteran quarterback Matt Schaub in a trade with the Houston Texans.
Woodley, who spent his first seven NFL seasons with the Pittsburgh Steelers, reiterated that he thinks Oakland, which lost six games by 10 points or fewer last season, will find a way to win close contests in 2014.
"Some games good in the first half, they just didn't close it out at the end of the game," the pass-rusher told 95.7 The Game. "So now we just have to learn how to close out games, and it'll be more wins than losses."
Several other Oakland newcomers echoed Woodley's sentiments Tuesday, the first day of the Raiders' voluntary offseason-workout program.
"Obviously, the record speaks for itself," Jones said. "I wasn't part of the team back then, but as we talked today, 4-12 is not good enough.
"When we played the Raiders in the past, we're kind of putting that 'win' on the board already. Now, everybody's got to look at their self in the mirror and we've got to understand that we really don't get no respect, and you're not going to get no respect when you're 4-12, so we've got to go out there and take it this year. And I believe we've got the right guys to do it."
Tuck, who won two Super Bowls during his nine-year stint with the New York Giants, also is excited about potentially reviving the Raiders.
"A lot of people always say you go to Oakland for your career to die," Tuck said. "I'm not looking at it like that. I'm looking at it like this is an opportunity to revive a storied franchise in a city with a great fan base behind this football team. The energy and excitement around this football team should be good. I'm excited about it."
ESPN.com Raiders reporter Paul Gutierrez contributed to this report.