Cody Garbrandt wants a piece of Bryan Caraway. Coming off his knockout victory over Thomas Almeida at UFC Fight Night 88, Garbrandt called out Caraway on Tuesday's edition of The MMA Hour, saying he wanted a fight with his fellow bantamweight contender at UFC 203 in Cleveland.

Caraway, though, has other plans.

On what was a momentous night for the bantamweight division in Las Vegas, Caraway had the biggest win of his career, as he handed the much-hyped Aljamain Sterling his first career defeat.

With four wins in his past five fights, Caraway believes he deserves either a title shot or a crack at one of the top names in the division. And he doesn't believe Garbrandt is quite yet on that level.

"I'm not saying [Garbrandt] wasn't talented, but, he wasn't in the Top 15 at all," Caraway said on The MMA Hour. "He had a good performance and all that, but I think that would be going backwards just from where I'm trying to go.

The way Caraway sees it, he just beat the fight ranked No. 4 in the division in Sterling, so Garbrant, despite his impressive performance, would be a step back.

"He just broke into the top 10," Caraway said. "I beat an undefeated guy that night as well. The No. 4 guy in the world. I want one of those top guys,I feel like I earned to fight for the belt. I beat the No. 6 guy before hat, I beat the No. 4 guy. I think Garbrandt, maybe one more top 10 win and he'll be ready for top five guys."

Whether you agree or disagree with Caraway's assessment of Garbrandt, it's hard to argue that Caraway hasn't earned his keep in the division. Caraway was the underdog going into the bout against Sterling, who was 4-0 in the UFC and in the first fight of a new contract.

Sterling got off to a strong start in the bout, too. While Caraway concedes he lost the opening round, in which Sterling thoroughly outgrappled him, he takes exception to the notion the round should have been scored 10-9.

"I didn't see a 10-8 round at all, Caraway said. "I think it would be absolutely ridiculous to be a 10-8 round. 10-8 round is when you beat somebody up and just are manhandling him..... I don't see how it was close to a 10-8 round. He didn't do any damage, I don't have a single mark on my face. 10-8 round I think you have to dominate somebody, beat them up, have them hurt. At no point in the first round was I even close to being hurt or finished."

It turned out to be moot, since Sterling took round one on 10-9 scores, and Caraway took over the fight in the last two rounds.

"The difference was, round one, he was afraid to punch and afraid to strike, but I was being just a little too cautious," said Caraway, who added that starting in round two, "I needed to do what I do best. I pushed the pace, pushed him against the wall, and got on top."

The bout, of course, had a little extra edge to it. Sterling had trolled Caraway hard on Twitter trying to get in the fight, using Caraway's relationship with UFC women's bantamweight champion Miesha Tate for fodder.

Caraway believes Sterling crossed that line, and wasn't about to act like he could just forget about it once the fight was over, saying, among other things, that Sterling's insults toward Tate were "misogynist."

"I respect people hyping the fight, but there's a certain part where, you know, he was being disrespectful," Caraway said. "He was disrespecting my girlfriend and her accomplishments like I should be ashamed of it. He's very misogynist and that's what I didn't like. It is what it is. It's not my tactic.

"I don't think he's very good at being witty," Caraway continued. "You know, Conor McGregor, that guy's extremely witty, I think his Irish accent kind of helps out a little bit. Hearing his voice makes everything a little bit funnier. But Aljamain, with me and my relationship, I've been hearing years of that, it's not cool to indirectly put Miesha down for being a strong, empowered woman, like I should be ashamed of my girlfriend. It's like, hey, buddy, she's more famous than you and 99 percent of the UFC's divisions so I don't know what you're trying to get that."

Caraway answered Sterling's insults in the best way he could, by winning when it mattered. And he believes after beating an opponent as highly ranked as Sterling, a title shot, or a fight that could get him there, should be next in line.

"They need new blood up there, they need a new face," said Caraway. "I guarantee of AS beat me, he's on a five-fight win streak, he beat all these guys. I beat the man, the top ranked guy, I believed I earned a title shot, and if not, I want to fighting someone who is right there in the mix. If I did have to go backwards, I don't want to go too far back."