The 37-year-old Kuroda said that he worked on all of his pitches in the start, and Yankees manager Joe Girardi complemented Kuroda's splitters and fastballs in particular.
"I know he gave up [three] runs, but that doesn't bother me," Girardi said. "I was pleased with where he's at physically right now. Everything I saw today from him, I was pleased."
Other than sharpening his pitches and making sure his stamina is ready for the regular season, Kuroda may not have much else on his to-do list this spring, as the owner of one of the two rotation spots that Girardi has absolutely guaranteed.
The other belongs to the Opening Day starter, CC Sabathia, and Kuroda is expected to slot somewhere behind the ace along with Ivan Nova and Michael Pineda, plus the winner of the fifth-starter derby between Phil Hughes and Freddy Garcia.
But looking to make a good first impression with his new organization, Kuroda said that any promises of security will not permit him to coast this spring.
"When I was in Japan, and also when I came [to the Dodgers], I don't think I've spent a season or a Spring Training without worrying if I will make the rotation," Kuroda said. "Even if [Girardi] says something like that, I don't think it's guaranteed. I'm always competitive and I'm always competing for my spot."
Girardi said he liked Kuroda's attitude, likening his professionalism to that showed by former Yankees outfielder Hideki Matsui.
"That's a good thing," Girardi said. "I think he wants to prove his value to the teammates, to the organization. I think there's some pressure when a Japanese-born player comes over here to play here; I think they feel a responsibility to really represent their country. I think he has always been about proving that he belongs here."
After Kuroda's clean first inning, Matt Joyce and Jeff Keppinger opened the second inning with singles to bring up catching prospect Stephen Vogt, who ripped a two-run triple down the right-field line and made Kuroda regret going against his catcher's suggestion.
"Russell [Martin] was asking for another pitch, but I wanted to throw a backdoor slider, and I just didn't locate the pitch really well," Kuroda said.
A Jose Molina groundout brought home Tampa Bay's third run, and Kuroda escaped without further damage, completing his 27-pitch outing with a strikeout of Elliot Johnson on a splitter.
Girardi said often last year that he enjoyed having Garcia's soft-tossing arsenal as a different look to a power rotation, and Kuroda's addition increases the off-balance feeling that opponents could have in a series.
"I think his split is different than what some of our guys have," Girardi said. "He's going to throw his share of cutters probably, as well. He starts with location of his fastball, but I really liked his split. I think you look at the couple of strikeouts today; both very good splits. It's a different look."
The Yankees anticipate that there may be a spike in Kuroda's ERA -- 3.07 last year in 32 starts -- as he adjusts to facing the American League East powerhouse clubs and pitching in Yankee Stadium, but Kuroda said that he is looking at this season as a challenge to impress his new teammates.
"They haven't seen me throughout the season, and they don't know what kind of pitcher I am," Kuroda said. "I think I have to prove something to everyone."