While Bareilles hears some "similarities" between the two singles, she told ABC News Radio that she and Perry are "on great terms and there's no issue there."
"Katy's a friend of mine and we've known each other a really long time, so she even texted me about it and we went back and forth," Bareilles said.
"The shame that I feel that's happened is that it's become a drama. It's putting this negative spin on two artists that are choosing to share positive messages," she added.
Bareilles pointed out, laughing, "If I'm not mad I don't know why anybody else is upset. I'm like, 'Relax, let's just celebrate that we can be out there and encouraging people to, like, feel strong and empowered.'"
The 33-year-old singer has more important things to focus on right now: she's kicking off a co-headlining tour with OneRepublic on Thursday night in Colorado.
"The whole thing sort of just made sense to me," Bareilles told ABC News Radio about teaming up with Ryan Tedder's band. "We've done a very limited amount of touring with them in the past, but we already know we get along great. And then I think just, musically speaking, it's going to be a great crossover. I know my fans. If they're not already familiar with them, they're just going to love what they do."
Bareilles predicted that there "probably" will be some sort of collaboration onstage between the two acts during the tour, and backstage, she said she'd love the chance to write some songs with Tedder during the tour.
"Ryan and I have done a little bit of back and forth in the past, and nothing has come totally to fruition," Bareilles revealed. "I dunno - I think we probably have really compatible writing styles and I think he's such a brilliant writer. … So, yeah, I would be really open to that."