"A hard-fought game for us," Sutter said. "I thought we had a good start. We did a lot of good things and we need to improve on some of those.
"If we lost 3-2 tonight in the shootout, I'd still be saying the same things," he said. "I said (Wednesday) it's a 3-2 league, and it was a 3-2 game."
Sutter was measured in his media scrum and deflected most of the attention away from his debut, although it was hard to ignore that he joined Ken Hitchcock of St. Louis as the only new NHL coaches among this season's six newcomers to win in their debut.
Sutter was just more than three minutes away from victory in regulation before Lubomir Visnovsky pumped in a shot from the right circle with Corey Perry screening Quick at 16:49.
The Ducks had only five shots on goal in the third period but secured at least a point with Visnovsky's heroics.
But Anaheim fell to 0-9-4 over its past 13 road games dating to their last road victory on Oct. 27. The Ducks have been outscored 48-22 in that period. Anaheim is 2-6-2 under Bruce Boudreau since firing Randy Carlyle on Nov. 30.
It was Brown's second shootout winner in as many games – he got the only goal in the tiebreaker for a 3-2 win at Toronto on Monday.
"I don't care how we do it," Brown said. "Right now it's about getting points. More importantly, we're starting to put some good games together."
Sutter, who is in charge of the forwards, drew a big laugh when told media he confused Mike Richards with Brad Richardson during his game-day preparation.
But Richards impressed with a goal scored in his return to the lineup from a head injury.
L.A. didn't score on the power play, but it had 34 shots on goal.
"I liked the way our forwards played, really good in all three zones," Sutter said. "That's what we're trying to do."
The teams were tied 1-1 before Brown connected on the Kings' second shot of the third period, ripping a snap shot from well above the circles that went top shelf on Jonas Hiller's blocker side. Drew Doughty started the play with a stretch pass to Anze Kopitar, who set up Brown neatly.
"It might not have looked like much, but the pass Kopi gave me," Brown said, "I don't know if a lot of guys can do that. It's a three-foot pass that goes a foot in the air and lands flat. I just got into position to shoot and put it in the right spot."
Anaheim took the crowd out of it through the first 30 minutes and took a 1-0 lead on Niklas Hagman's re-direct. Hagman positioned himself on the left side of the crease and got his stick on Visnovsky's shot at 13:55 of the second period.
Hagman, whom Sutter traded for when he was general manager in Calgary, has four goals in five games playing on the top line with Ryan Getzlaf and Corey Perry.
But Richards shake the home crowd alive with a play that demonstrated his value to the Kings. He won a faceoff to the right of Hiller, drifted toward the net and tipped Drew Doughty's point shot at 16:17 for his team-leading 12th goal and a 1-1 tie.
Anaheim had a full power play in overtime but couldn't score.
"I thought for sure when we got that power play in the overtime that it was going to happen," Boudreau said.
"It didn't. Then they got it (a 30-second power play) and I thought, ‘Uh-oh.' This is what usually happens and then when we killed that off I thought, ‘I don't care, we are going to win it in the shootout. I mean, the shootout is a crapshoot – anything can happen with it.
"Overall, I hate to keep saying it but I thought we played pretty solid. The difference between winning and losing is sometimes just the attitude and believing that you are going to win or believing you are going to lose."
The Kings might start believing under Sutter. They are playing the same system they did under Terry Murray, but there was a different feel.
"I think there's a renewed energy with hearing a new voice," Brown said. "The Xs and Os are a lot of the same, it's just a lot of things are different. It's hard to explain, but it's just a different feel behind the bench."
Said defenseman Matt Greene, "He's more animated. He's more vocal than Terry was. It's different, for sure."
The Ducks' slumping penalty killing unit, which previously allowed 10 goals in 32 chances under Boudreau, killed two penalties early in the second and a slashing infraction by Getzlaf spread over the second and third periods.
The Kings appeared to have a jump in their step for their new coach at the start but neither team impressed during an unremarkable opening period.
Hiller kept it scoreless with consecutive stops Brad Richardson and Kopitar. The Ducks had two power plays but failed to register a shot on goal.
Sutter improved to 31-15-5 all-time against Anaheim, the second-most wins by him against any club behind Edmonton.