Cal Petersen made 32 saves for Los Angeles (36-23-9), which is two points ahead of the Edmonton Oilers for second in the division.
"It's hard to pinpoint just one thing," Kings captain Anze Kopitar said. "It was a lot of stuff that, obviously, didn't go right and we didn't do right. So this one definitely stings, especially the time and position we're in. It's a hard one to swallow, but at the same time, we're leaving for three very important games on the road, so we'll address this one, I'm sure, look at some stuff tomorrow and put it behind us and get ready for the next one."
Los Angeles will begin its three-game road trip against Edmonton on Wednesday.
"We have a tough task on hand," said Kings coach Todd McLellan, who became the 31st person in NHL history to coach 1,000 regular-season games. "It's not about my memories or what I liked or didn't like there. It's about fixing what we did wrong today and playing better there because we're going to have to."
Chris Driedger made 36 saves in his first start since March 10 for the Kraken (21-39-6), who lost 4-2 to Los Angeles on Saturday.
"You know, we just looked like a complete hockey team out there tonight," Driedger said. "It's great to see those guys come together. Tons of communication, tons of energy and seems like we were just sick of losing."