They tied it 2-2 on Saturday when Slavin scored off a pass from Jordan Martinook at 9:50 of the third period.
"Anytime you have a lead, you want to keep pushing, but you don't want to push and not have support coming back," Holtby said. "We just got caught there a little bit, especially against a team that transitions so fast."
Hurricanes coach Rod Brind'Amour said, "We weren't playing a poor game. We were pretty solid. We had a couple, I thought, bad breaks there and the guys just hung in there, and then obviously some huge penalty [kills] in this game. I think that was the story of the game for me."
Carolina was 1-for-4 on the power play. Washington was 0-for-6.
"We just didn't execute what we wanted to do," Oshie said of the power play. "When you don't do that, and you're not winning too many battles down low, the other team's PK is going to send a lot of pucks down the ice, and that's a lot of skating for a power-play unit."
The Capitals made it 1-0 with 2:37 left in the first period when Hathaway controlled a loose puck in the left circle and shot over Reimer's left shoulder.