White, who was a guest on "ESPN First Take," discussed the Falcons' change in mentality after their NFC Championship Game loss to the San Francisco 49ers last season.
He said that until last season the Falcons were "satisfied" with just making the playoffs.
"I think that the first three [playoff appearances under coach Mike Smith] we were getting there and were just having fun being there. And then we turned a curb, and we said we have to stop just getting there and we have to win games," White said.
"We're ready to take that next step. We know how good our football team is and the players we got, so it's either Super Bowl or nothing for us right now."
"Nothing else. Anything short of that is not a good season for us right now," he said.
Later in the interview, White was asked to rank his top five NFL teams heading into the 2013 season. He ranked the Seattle Seahawks No. 5, the Denver Broncos No. 4, the New England Patriots No. 3, the 49ers No. 2 and the Falcons No. 1, despite their NFC title-game loss to the San Francisco last season.
"I feel like we’re a better football than the San Francisco 49ers," he said, adding that turnovers were the reason the Falcons fell in the NFC Championship Game.
He said he's confident in his team because he sees growth in his teammates.
"... Every year I see growth all over our team. That’s the biggest thing when you’re dealing with football players. If they're growing every year, you're getting better," he said.
The 49ers overcame an early 17-0 deficit, then stopped the Falcons on fourth-and-7 from the 10-yard line with 1:13 remaining to seal a 28-24 victory. Ryan attempted a pass over the middle to White that would have been enough to keep the drive going. But linebacker NaVorro Bowman stuck a hand in to knock it away.
White said the play was designed to go to him, but the 49ers played a coverage they had not used previously in the game, surprising Ryan and the Falcons.
"We just got outcoached on that one play," White said.
He said it's unfair to blame Ryan, whom he called an "excellent quarterback," for the Falcons' failure to convert the fourth down.
"It takes so much more than just Matt Ryan to finish plays, especially down the stretch. You can't just put it on the quarterback and say, 'All right, you have to make this one play to get over the hump.' It has to be me, it has to be Julio, it has to be Tony. We have to go out and make those plays and make it easier on Matt Ryan," he said.
The one big change the Falcons have made to the offense is releasing running back Michael Turner and signing Steven Jackson to fill his role. White said Jackson will give the Falcons' offense a new dimension.
"I think [Jackson's] an upgrade because he's a three-down back," White said, saying Jackson's presence helps the Falcons mix up the play calling.
"When you have a guy like that, nothing changes. You just go out there and play. The defense has to guess and try to make a guess at what you're doing ... is it run? ... is it pass? It will be a whole lot different."
Information from The Associated Press was used in this report.