Karlsson was second in the voting and Hedman third.
"Those two guys are guys I love to watch and learn from every night," Burns said.
This was a transformative campaign for Burns, who was considered by some up until the final quarter of the season to be a strong candidate for the Hart Trophy, awarded to the League's most valuable player.
Burns, 32, had 76 points (29 goals, 47 assists) in 82 games, leading defensemen in goals and points. On Feb. 18, he had 27 goals but didn't score for 16 games. During his scoring drought the Sharks fell out of first place in the Pacific Division and finished third at 46-29-7.
Hedman, 26, led NHL defensemen in assists (56) and was second behind Burns with 72 points in 79 games. Karlsson, 27, had 71 points (17 goals, 54 assists) in 77 games, third among NHL defensemen after finishing first with 82 in 82 games in 2015-16.
Burns was impressed with what Karlsson and the Senators did in the playoffs, reaching the Eastern Conference Final.
"They had something special going on," Burns said. "You have to have that magical run going. Nashville had it. I think we had it the year before where just something kind of clicks and becomes fun and easy almost."
The Sharks signed Burns to an eight-year, $64 million contract extension on Nov. 22. His Norris Trophy win came almost six years after the Sharks acquired Burns (June 24, 2011) in a trade from the Minnesota Wild, who took him in the first round (No. 20) of the 2003 NHL Draft as a forward but converted him to defense.
Last season Burns had 24 points (seven goals, 17 assists) in 24 playoff games when the Sharks advanced to their first Stanley Cup Final before losing to the Pittsburgh Penguins in six games.
Burns went out of his way to praise his defense partner Paul Martin.
"I can't say enough about Paulie Martin and how he's helped me in my game on and off the ice," Burns said. "On the ice he's making great plays, he's always in great position. He's been huge for me."
The Sharks lost to the Edmonton Oilers in the Western Conference First Round this season. While Burns is thrilled with the Norris, he made it clear there is unfinished business in San Jose.
"At the end of the day, San Jose wants a different trophy and that's the one we're going to try to get," he said.
Pts. 1st-2nd-3rd-4th-5th
- Brent Burns, SJS 1437 (96-61-10-0-0)
- Erik Karlsson, OTT 1292 (63-86-9-4-3)
- Victor Hedman, TBL 728 (3-13-106-21-14)
- Duncan Keith, CHI 384 (2-4-19-70-31)
- Ryan Suter, MIN 175 (2-1-9-25-28)
- Shea Weber, MTL 100 (1-0-6-11-27)
- Drew Doughty, LAK 51 (0-0-1-10-16)
- Mark Giordano, CGY 41 (0-0-1-11-3)
- Dougie Hamilton, CGY 23 (0-0-0-6-5)
- Justin Schultz, PIT 22 (0-0-2-2-6)
- Roman Josi, NSH 19 (0-1-0-2-6)
- Dustin Byfuglien, WPG 15 (0-0-2-1-2)
- Jared Spurgeon, MIN 14 (0-0-2-1-1)
- Kevin Shattenkirk, WSH 9 (0-0-0-1-6)
- Torey Krug, BOS 7 (0-1-0-0-0)
- Alex Pietrangelo, STL 7 (0-0-0-1-4)
- Ryan McDonagh, NYR 5 (0-0-0-1-2)
- Seth Jones, CBJ 4 (0-0-0-0-4)
Zach Werenski, CBJ 4 (0-0-0-0-4)
- Jaccob Slavin, CAR 2 (0-0-0-0-2)
- Cam Fowler, ANA 1 (0-0-0-0-1)
Dmitry Orlov, WSH 1 (0-0-0-0-1)
Marc-Edouard Vlasic, SJS 1 (0-0-0-0-1)