The home run followed Rivera's loss to the Angels two nights earlier and a blown save against the Boston Red Sox on Sunday.
Yankees manager Joe Girardi isn't concerned, though.
"I've seen Mo have three or four bad days, then run off a long streak," Girardi said. "I don't think all of a sudden Mo's forgotten how to pitch. He's had a little blip on the radar screen, but he'll get back on track."
Girardi said Branyan's homer -- a no-doubt shot to right field -- was simply a mistake.
"He missed his location," Girardi said. "That's going to happen. As much as we want to think he's about as close to the perfect closer as we've ever seen, he's not perfect."
Center fielder Curtis Granderson said he's not worried about his teammate and feels talk of Rivera's troubles is being blown out of proportion.
"There's always going to be a story," Granderson said. "In baseball especially, there has to be a reason why, instead of just giving credit to the guy who hit the ball."
Granderson said Rivera doesn't seem different and hopes the media and fans can look at the bigger picture.
"The main thing I think people need to focus on is that, yes, he gave up a home run," he said. "It goes from a four-run lead to a one-run lead, and then he just shuts the door.
"A lot of guys in that situation could panic, make another mistake and lose the game but, sure enough, he ends up with a save."
Rivera said he "isn't concerned at all," about his velocity, mechanics or health. He said the mistakes have been just that -- mistakes.
"Those things are going to happen," the closer said. "It's about how you react to those things. Whatever happens, happens. You have to put it behind you."
Rivera's goal whenever he does make mistakes, he said, is to focus on doing his job and getting the next out. When that doesn't happen, he tries to shake it off.
"I'm not happy, but it won't make me or break me," he said.
Girardi joked that he'd only be concerned if Rivera kept giving up runs for a month straight, but, until then, he won't worry.
"My guess is he'll get on track," the manager said. "He's one of the greatest closers of all time."