"I feel fine," Cozart said. "I saw the docs and I'm going to get monitored throughout the night and just let Paul know. Obviously, I had a little headache getting hit like that. It's a little pressure up in the head. I took the test and everything went well. [Tuesday] I think everything should be OK."
At no point, Cozart said, did he lose consciousness.
"It just got away from him. I don't even really remember, to be honest with you," he said of the Billingsley pitch. "I just remember it being loud and I had some ringing in my ears. I feel a lot better than I thought I was going to be. That's a positive.
"After the ringing left, I kind of sat there and Paul said, 'How are you doing?' I think I'm actually doing pretty good."
When the ball struck Cozart, it bounced hard off his helmet and went several rows behind home plate. Cozart said he was told that his helmet was cracked.
"It was real loud," Baker said. "It reminded me of when Goose Gossage hit Penguin [Ron Cey] in the  World Series. I was on deck. That's how loud it was.
"They gave [Cozart] all the tests. We took him out for precautionary reasons. He was a little glossy-eyed."
Both teams knew the pitch was unintentional.
"I was trying to throw a two-seamer and it got away from me," Billingsley said. "Definitely not the outcome I wanted."
Cozart, 26, was 2-for-2 in the game with two singles and is batting .250 with eight home runs and 16 RBIs. His absence put a shorthanded Reds club in a bigger bind. The team is already playing without injured regulars Joey Votto and Scott Rolen. Baker was not sure if a roster move would be needed. The Reds have the option to put Cozart on the seven-day disabled list for head injuries.
At this point, however, it was just a frightening incident that Cozart was lucky to walk away from.
"I've been [hit] before, a couple of years ago in the Minor Leagues and it was actually worse in the Minor Leagues because it got me under the helmet," he said. "This one was scary. It was so loud when it hit the helmet. It's kind of like a blur. I see the ball coming and you're just trying to get out of the way as soon as possible. I just couldn't get out of the way."
Mark Sheldon is a reporter for MLB.com. Read his blog, Mark My Word, and follow him on Twitter @m_sheldon. This story was not subject to the approval of Major League Baseball or its clubs.