GLENDALE, Ariz. -- Sandy Koufax arrived in Dodgers camp for a third consecutive year on Thursday, and after watching some bullpen sessions the Hall of Famer talked about various things, including Clayton Kershaw.

Kershaw is coming off two consecutive Cy Young Award-winning seasons that ended with elimination at the hands of the Cardinals in playoffs. In both series, Kershaw lost twice.

"If somebody had told me anybody would beat Clayton twice in one series, I would have said, 'No way.' I probably would have cursed. But, it happens," Koufax said. "I have to say, if you heard his speech, that last line is as classy as it gets. On a night you're being honored to bring up something that didn't go right, that was pretty special."

Koufax referred to Kershaw accepting both his National League Cy Young and MVP Awards at the BBWAA dinner in New York in January. Koufax, like last year, introduced Kershaw, and at the end of a series of thanks Kershaw brought up St. Louis.

"My last thank you goes to the St. Louis Cardinals," Kershaw said in his speech. "Thank you for reminding me that you're never as good as you think you are."

Last week, Kershaw was asked about his speech.

"Those awards mean a lot to me, but I'm not oblivious to the fact that we didn't win the World Series," Kershaw recalled. "I just wanted to make sure I got that point across."

After losing twice to the Cardinals in the 2013 NLCS, Kershaw struck out 13 in seven scoreless innings in a win on June 29, then struck out eight and allowed three runs in seven innings in St. Louis on July 20. But then the Dodgers lost to the Cardinals in the 2014 NLDS, with the Dodgers and Kershaw losing leads in the seventh inning of both Games 1 and 4.

"I was really glad in the middle of the season when he shut them out, I thought he proved he could beat them. It just didn't happen. Just bad timing," Koufax said. "The games were turned around. The first one he got enough runs to win, the second one he didn't. If they were turned around it might have been different."

Kershaw in the 2014 NLDS allowed two runs on three hits and two walks, with 17 strikeouts combined in the first six innings of each of his starts, but then allowed nine runs on nine hits in the two seventh innings, while recording just two outs.

"He just ran into two tough innings. He dominated them for 12 innings in that series. He ran into two tough innings against one of the best grinding teams there is," catcher A.J. Ellis said last week. "I don't think he has anything to prove anymore other than being the best pitcher of our generation."

Kershaw is 1-5 with a 5.12 ERA in his postseason career. But Koufax doesn't think the poor October mark will take away from Kershaw's legacy.

"I don't think so. Because I think he'll be in a lot more postseasons and I think he'll totally turn it around," Koufax said. "The best pitcher in baseball is not going to have that happen. Probably never again."

Do the last two Octobers push Kershaw even harder?

"I don't know if he has any extra fire burning. He always has a lot of fire burning. He's a great competitor," Koufax said. "Will there be any extra? I hope not, because extra might destroy him. You can just go so far. One hundred percent physical effort will kill you because there’s no room for thinking. You can go to 99 percent but you have to leave some room for the brain."

Manager Don Mattingly had a similar refrain last week.

"I don't think anything changes with Clayton. He goes about his business like he has in the past," Mattingly said. "Any situation that he's been through he's going to learn from. I think he's going to continue to get better and better."

Kershaw may not use those Cardinals losses for motivation for his 2015. But at the very least it is in the back of his mind. And it's not something he can change, correct or exorcise until the playoffs.

"You want to make up for everything that didn't go well in October, but you can't do that in April," Kershaw said. "You have to wait for it first."