The Rays pitchers earned their fines by tweeting about the incident after the game, a violation of baseball's social media policy, which prohibits comments that "denigrate" an umpire.
"I didn't know Hallion got fined," Price told reporters on Thursday. "It's part of it I guess. Something you obviously want to stay away from. You don't want to donate money to whatever it goes to. I'd rather give it to my foundation or something like that. But it's part of it. I could have chosen a better way to handle it. But I feel like I handled it pretty well."
Price accused Hallion on Sunday of using an obscenity when telling the reigning Cy Young Award winner to throw the ball over the plate. Hallion denied such following the contest and told a pool reporter: "I'll come right out bluntly and say he's a liar."
Price said he derived no satisfaction from Hallion getting fined.
"Honestly, that's not what I wanted," Price said. "I didn't want him to get fined. I didn't want him to get suspended. I wanted an apology. That's all I cared about. Whatever happened to Hallion, I just wanted an apology. I didn't want any money to come out of his pocket, I didn't want him to get fired or fined or suspended or anything like that. I just wanted what I thought was fair to me and the rest of the team, and that was an apology."
Price responded "no" when asked if he had received an apology from Hallion.
Price, who is an active Twitter user with approximately 150,000 followers, tweeted from his account late Sunday, @DAVIDprice14: "Someone please give me the definition of accountability…" and "Someone give me the definition of a coward please." Based on his use of Twitter and his relationship with Major League Baseball, Price also was miffed with Major League Baseball.
"I didn't think I directed my tweets toward anybody," Price said. "So I guess they just kind of assumed. I'm sure there could be ways around that. ... As many times as MLB asks us to tweet things for them, I find it kind of funny. It's fine. I'll remember this the next time they ask me to do something. I don't feel like we were in the wrong and we got mistreated. ... I didn't direct my tweets toward anybody."
Moore noted that "$1,000 does sound like a lot for a tweet."
"It is what it is," Moore said. "I would just love for it to be over like it never happened. I think it's kind of catching a little bit more than it needs too. … I definitely would rather this not happened and just stayed away from all of it.
"… I don't even tweet that much, so for me to get in trouble over something like that is pretty irritating with myself. My job has nothing to do with my Twitter account or anything that goes on on the field. I'm not going to let that happen again."
When asked if he was aware of MLB's social media policy, Moore responded, "I am now."
"I figured you couldn't say certain things," Moore said. "I didn't know that that was exactly degrading. It is what it is. It's over."
Hellickson, who also was ejected from Sunday's game, said he thought the fine was fair, but he added: "I honestly don't really know if anybody's ever been fined for tweeting."
Hellickson did not know yet if he would be receiving an additional fine for being ejected.
"I definitely feel it was important to have [Price's] back on the field," Hellickson said. "Saying something on Twitter, that probably wasn't the right thing to do. A thousand dollars is a lot of money. Wish I wouldn't have done it now."
Hellickson smiled when asked if he had repented.
"I have," Hellickson said. "You won't hear me yelling anymore."
Rays manager Joe Maddon said he wanted the entire episode to die "a quick death."
"It gained way too much traction," Maddon said. "And again, a lot of it has to do with the social media component of the world we live in today. And that kind of exaggerated the impact I think. And all of a sudden you do develop a situation that has to be tended to.
"I also believe that maybe everybody is going to learn from this and hopefully be able to avoid this in the future, the fact that it's not the right way to go about disputing a situation."