Manning received 33 votes for the offensive player honor. He also was runner-up last year to Peterson for the award.
This time, running back LeSean McCoy of Philadelphia was second with 10 votes, followed by Kansas City running back Jamaal Charles with four.
Carolina grabbed two major awards, with Ron Rivera winning AP NFL Coach of the Year and linebacker Luke Kuechly voted top defensive player.
Rivera engineered the Panthers' turnaround from a 7-9 record to 12-4, the NFC South title and a first-round playoff bye. Kuechly keyed a defense that allowed 241 points, less than every team except NFC champion Seattle.
"I had no idea," he said of adding the award to the top defensive rookie honors he got last season. "You look at the list of guys: Robert Mathis, a sack master, a guy that forced a lot of fumbles. And obviously, everybody knows about Richard Sherman and Earl Thomas. Those guys are both studs."
Green Bay running back Eddie Lacy and Jets defensive tackle Sheldon Richardson were the top rookies for 2013.
San Diego quarterback Philip Rivers took the Comeback Player of the Year award at the NFL Honors show.
Rivera's fine work in his third season in charge in Carolina brought him 21½ votes. That outdistanced Kansas City's Andy Reid, who got 13½ votes. In his first year with the Chiefs, Reid took them from 2-14 to 11-5 and an AFC wild-card berth.
"I do feel a lot of pride because it has been a long journey, but it also was a part of the process," Rivera said. "Just like us getting to where we are winning 12 games was part of the process. We started, the team was 2-14 before I got there and we went to 6-10 and then 7-9, and this year we broke through at 12-4. It was part of the process of growing and developing."