Niemann allowed himself a smile about becoming a historical footnote for Jeter's accomplishment.
"At least he had to bunt on one of them," Niemann said. "That makes me feel a little better."
Upton, who recently suffered an ankle sprain, didn't get back in time to make the catch on the ball Jeter hit that turned into a double.
"Just couldn't get there," Upton said. "If I'm 100 percent, maybe 95, I would have gotten there. But [his ankle] just wouldn't let me get there."
When it was pointed out that Gehrig's record might have held for another day or two had he made the play, Upton smiled.
"Yeah, but it did happen and congratulations to him," Upton said.
Inside the visitor's clubhouse, there were only positive remarks about the Yankees captain.
"I'm really happy for [Jeter]," Rays manager Joe Maddon said. "I got to know him a little bit during the All-Star Game -- truly a nice man. He carries himself in a manner that is worthy of passing Lou Gehrig here on the all-time hit list."
Rays outfielder Carl Crawford said Jeter has everyone's utmost respect.
"He's been doing it so many years, the championships, playing for the Yankees, the way he handles himself on and off the field," Crawford said.
"He's just one of those guys you look up to and respect. Try to watch him and pattern yourself after him a little bit. He's very professional. I can see why he's had the kind of success he's had."
James Shields echoed Crawford when he called Jeter "very professional."
"He doesn't show anybody up, he runs hard down the line every time," Shields said. "There's no doubt about it, he's one of the classiest players in baseball. I've been watching him ever since he first got called up. I knew he was a pretty special player. But then when I finally got up to the Major Leagues, I realized what a great player he is.
"He's a very unselfish player. He executes pretty well. And, for my opinion, he's one of the top hitters in the league every year, hands down. In my opinion, he's going to go down as one of the best Yankees ever. It's amazing to watch him pass all those Yankee icons. That's pretty special."
Upton called Jeter "pretty much unbelievable."
"He's got all the world championships you could ask for," Upton said. "He's done it under pressure and in one of the toughest markets to play in in baseball. And he's just carried himself so well all the way through it.
"A lot of times you don't even know he's there, when a lot of guys of his stature would let you know. He's kind of an under-the-radar guy. He goes out there and does his thing with class."
Maddon was also in Baltimore the night Cal Ripken Jr. broke Gehrig's consecutive games played record.
"Seems like I'm always around this time of the year, when significant records are broken," Maddon said. "... So maybe it's great, great baseball players are built to break records at this time of year and I'm supposed to be in attendance somehow. I was born underneath that astrological sign."