The Yankees had looked poised to force a game six after dominating the early innings to race into a commanding 5-0 lead at Yankee Stadium.
But defensive blunders allowed the Dodgers to pile on five unearned runs in the fifth inning to tie the game before further mistakes contributed to them taking a winning 7-6 lead.
"As I said to the guys, obviously it stings now," Boone said after the defeat. "But this is going to sting forever."
The Yankees fifth' inning meltdown began with captain Aaron Judge dropping what should have been a routine catch in center-field.
"We just didn't take care of the ball well enough in that inning," Boone said. "Against a great team like that, they took advantage."
Boone meanwhile could not hide his disappointment at the abrupt ending of a season that had brought the Yankees tantalisingly close to a first World Series crown since 2009.
"I'm heartbroken," Boone said. "It doesn't take away my pride of what that room means to me and what that group forged this year and what we've been through to get here.
"But I'm heartbroken. I'm heartbroken for those guys that poured so much into this. The ending is cruel. It always is.
"I'm 51. I poured my life into that. You're chasing that, and when you get that close, it's heartbreaking."
