According to Elias Sports Bureau, it was the only game in major league history in which a pitcher struck out as many as 15 batters without allowing a hit or a walk.
But Kershaw said he wouldn't cast a vote for his as the all-time best if he had one.
"I always think about it as far as circumstances," Kershaw said Friday. "So, a game in June always matters, but when you think about Don Larsen pitching a perfect game in the World Series and stuff like that, I think the ramifications of the game are more important than a June game necessarily."
Kershaw very well might have had a perfect game -- the 24th in baseball history -- had Dodgers shortstop Hanley Ramirez not made a throwing error to lead off the seventh inning. Only three balls left the infield all night.
The only other difficult play was when Miguel Rojas fielded a sharply hit Troy Tulowitzki grounder behind third base and threw him out. Rojas' momentum carried him into foul ground.
There have been seven games in major league history that fell short of a perfect game because of one error. Kershaw's was the 283rd no-hitter.
Dodgers manager Don Mattingly, who played in no-hitters thrown by Dave Righetti and Jim Abbott, said he wasn't qualified to weigh in on the debate of all-time greatest.
"You're splitting hairs when you get to that point," Mattingly said. "The fact he strikes out 15 and doesn't walk anybody and does it in 107 pitches tells you how dominant he was. He had the whole package working. Is it the best of all time? Obviously, a lot more people know all the games better than me, but it was obviously pretty good."
The ball Tulowitzki hit, as well as Kershaw's cleats and the scorecard kept by Dodgers spokesman Joe Jareck will be shipped off to the Hall of Fame in Cooperstown.
Kershaw said among the flood of well-wishes he received after the game were a text message from Dodgers legend Don Newcombe and voice mail messages from co-owner Magic Johnson and Hall of Famer Sandy Koufax.
"[Koufax] and Magic both just said, 'I'm proud of you and it was fun to watch,' that type of stuff," Kershaw said.
The ace left-hander said he was asked before he threw the no-hitter to tape an appearance on Thursday for the "Jimmy Kimmel Live" show, but that the producers canceled his appearance before Wednesday's outing in favor of visits by members of the NBA champion San Antonio Spurs and Stanley Cup champion Los Angeles Kings.
And he didn't get a call back from the show after his no-hitter.
"That's OK. I'll go on that show anytime," Kershaw said.