Instead of out on the field, he was with a few of his fellow pitchers in the Dodgers' training room icing his left arm -- the arm which threw 6 2/3 innings of two-run ball to keep the Dodgers in position to mount a rally.
It was a hidden location for a celebration. But when you consider how the wild ninth inning overshadowed his outing, the anonymity of it all makes sense.
Kershaw stood toe-to-toe with Cardinals co-ace Adam Wainwright for six innings -- but he earned a no-decision.
He allowed just two runs as the 11th youngest pitcher in Major League history to start a playoff game -- yet he left the game on the hook for a loss.
While Kershaw's effort might have gotten lost amid all of the highlights, it wasn't forgotten by his teammates.
"He's not going to back down -- he hasn't ever before," right fielder Andre Ethier said. "He impresses me it seems like almost every other day," catcher Russell Martin said. "His character and how mature he is for his age. And he doesn't back down from anything -- that's just his mentality."
Kershaw's reserve was evident right from the opening pitch.
Teammate Randy Wolf had already shown how the postseason could get to a veteran pitcher the previous night. In his first career playoff start, Wolf had a rocky first inning that luckily ended in just one run scored by the Cardinals.
Kershaw on the other hand -- all of 21 years and 203 days -- came out and retired St. Louis 1-2-3 in the top of the first.
He did endure a rough stretch in the second inning: a Matt Holliday home run and then back-to-back singles.
But Kershaw calmed himself down and struck out Mark DeRosa and forced Colby Rasmus into a double play to escape the jam.
"I was very comfortable watching Kershaw pitch today," Dodgers manager Joe Torre said. "I thought he responded to the challenge very, very well."
Others didn't hesitate to throw praise in Kershaw's direction after the game, but the left-hander was lukewarm in evaluating his performance.
"It was OK," Kershaw said. "Wainwright, he's going to be the Cy Young [winner] for a reason. Anytime you pitch against a guy like that, you know you can't give up too many runs and I made a couple of mistakes."
One of the gaffes was an errant seventh-inning pitch that Rasmus hammered for an RBI double to give St. Louis a 2-1 lead.
And that hit probably made Kershaw reluctant to pat himself on the back for a job well done.
"I came out of the game losing," he said. "When you're pitching in the postseason, you want to give your team a chance to win, and coming out of the game losing is not what you want to do. ... "
"I did all right. I'm not saying I didn't do fine, but it could have been better."
It's that attitude that causes Torre to insist over and over that Kershaw isn't your average 21-year-old.
And that attitude might have made it easier for Torre to justify leaving him in the game for the seventh inning after he had thrown 97 pitches.
In the regular season, Torre probably opts for a reliever in that situation -- Kershaw didn't start too many innings this year with a pitch count that high -- but Kershaw had proved that he isn't fazed by a big stage.
He threw six shutout innings last Saturday against Colorado in the Dodgers' NL West-clinching victory.
And though Kershaw gave up a run in the seventh, he's shown he can be trusted in those moments.
"When the pressure rises," Martin said, "he gets better with it."
David Ely is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.