There was one of verbal affirmation, with manager Mike Matheny sending both players home not just with a to-do list but also a reminder that the Major League club still valued them.
Then there was the point implied through the Cardinals' subsequent activity. Within a four-day span in November, Jay and Kozma -- both starting position players last year -- no longer had assurances of regular playing time. General manager John Mozeliak did not mince his words, either. Subpar results from the shortstop and center-field spots in 2013 necessitated that the Cardinals made additions in both areas.
For Jay and Kozma, their place in the organization would be determined on which message resonated more. The verdict?
"I've seen them handle it like pros," Matheny said on Sunday. "They couldn't have handled it much better."
Neither Jay nor Kozma had a chance to prove the payoffs of their offseason work before the Cardinals bumped both down the depth chart. The starting shortstop job is now Jhonny Peralta's. Even a bench spot will be tough for Kozma to find with Mark Ellis and Daniel Descalso in the mix.
Jay won't end up back in Triple-A, but he's likely to spend much more time on the bench. Best-case scenario for him would be to open the season with a timeshare in center.
For two players who combined for 1,076 plate appearances and 254 starts last season, it's bound to be a transition. They left camp a year ago as starters on a postseason-bound club. Now, they're merely seeking a fit.
"We've gotten a lot better by acquiring guys. That's what you want," Jay said. "It's easy for me. All you think about is October. You think about those playoff experiences. You think about going to the World Series and being a part of these special teams where hopefully in 10 or 15 years we talk about the great run we've been on. It's easy for me to put that [individual stuff] aside and just really focus on the team."
Both players entered the offseason knowing that future playing time would hinge predominately on whether they could improve with the bat. Kozma needs to offer more offensive production to complement his above-average defensive ability. Jay's defensive deficiencies could be better veiled with more consistency at the plate.
The two tried a series of in-season adjustments in 2013 but found it difficult to tweak mechanics in a setting where results were scrutinized. It was in pressure-less environments where the work was finally able to get done.
Kozma spent his winter days on the campus of Oral Roberts University, where he tried to right all that went wrong during the second half of the 2013 season. He practiced a shorter swing and was intentional about keeping his front side closed longer. It was his tendency to fly open that had caused him to pull so many pitches.
"Mechanically, things fell apart during the season," Kozma said. "It's pretty tough because I felt like I was doing things one way throughout the first half, and then they started pitching me differently in the second half and I couldn't adjust because my mechanics were off. It was probably one of the toughest that I've ever had at any level."
Kozma finished the season with a .217 average. His slugging percentage of .273 was the lowest of any player at any position in either league who logged at least 350 plate appearances. He had an OPS+ of 54. Though the Cardinals had one of the National League's best offenses, it became tough to hide Kozma in the bottom of the lineup by season's end.
"You practice in game time, so sometimes the results sometimes are not what you want," hitting coach John Mabry said. "But sometimes you have to go backwards to go forward. The thing is that you have to have the ability to give it time. It's tough to be playing a highly demanding position like shortstop and make these adjustments. It really says a lot about how tough he is mentally because to be asked to do that and still compete defensively [is difficult]."
Kozma delivered a pinch-hit single on Saturday, and he went 1-for-2 with a two-run double on Sunday.
"It's a little different than last year," Kozma said. "I'm going to have to compete and fight for a job. But that's why we're all here. We're here to try to make a big league team. If I don't, so be it. But I'm out here trying my best to make this squad."
Jay was exposed offensively and defensively in 2013, though he salvaged his starting job by batting .308 over the final three months. Still, he fought with his swing throughout the year.
In late April, he attempted to reduce the amount of movement in it. That worked for a while, but Jay eventually went back to his old ways. With offseason work in Miami this winter, Jay has made "some obvious adjustments," to use Matheny's words, to make his setup simpler.
"He knows what is at stake," Mabry said. "He has a good mindset. He's not going to let the game outwork him. He understands what it takes because he's been here a few years. Right now he has a really good idea of where he's at and what he's doing. Again, it's another case of the repetition part of it is a lengthy process. Until you get comfortable and trust the work that you did in a game speed situation, that's the test of all tests."
Jay entered Sunday with one hit (a single) in his first three spring at-bats. The two outs he hit into would have both gone over the fence had the wind been blowing another direction. It's been enough to get Matheny's attention.
Jay has made an impression on the backfields and in the clubhouse, too, where he continues to assert himself as a leader despite no guarantee of playing time.
"We've all seen that where a guy says, 'OK, this group has given up on me,'" Matheny said. "We made sure we told them, 'Just make sure you stay the course. Just keep working on what you're working on. This stuff will take care of itself.' You can't control what's being said. All you can really control is how you handle this, first off. And two, just come out and work. If it takes you proving people wrong, if that's your motivation, then jump all over it. Come back with a plan on how you're going to continue to get better.'
"Both of them are very capable Major League players. And I see more upside. I see better [upside] than we have ever seen before in them."
Jenifer Langosch is a reporter for MLB.com. Read her blog, By Gosh, It's Langosch, and follow her on Twitter @LangoschMLB. This story was not subject to the approval of Major League Baseball or its clubs.