Byard said he met with Titans coach Mike Vrabel about his decision to celebrate an interception on Monday night by running to the 50-yard line at AT&T Stadium and dance with his teammates on the Dallas Cowboys' star logo.
Vrabel on Tuesday expressed his disappointment with Byard's actions.
"Some people loved it, some didn't, but the main thing is the head coach didn't like it, and that's the most important thing," Byard told reporters, according to the team's website. "I am more concerned with the trust and the way my head coach and my teammates view me. Those guys know that I am not a selfish person, and I understand that act looked selfish and that's why we had a talk about that.
"I don't want to be in the doghouse, or end up in the doghouse over a celebration. But we're good. We're good."
Vrabel said on Tuesday he wanted his team to "celebrate with a teammate, find somebody else in a Titans uniform. Find a coach, and celebrate with them. But we don't need to do that. It's not what we want to do."
Byard said Wednesday that's exactly what he'll do next time when he wants to celebrate a big play.
"It's something I thought about before that was going to be kind of fun, to get the sideline riled up a little bit," Byard said, according to the team's website. "But at the end of the day, next time for sure I am going to go find my teammates, maybe find Logan Ryan, who helped me make that play, and celebrate with him first."
Byard's celebration was reminiscent of a similar display by former San Francisco 49ers wide receiver Terrell Owens, who celebrated on the star twice in a game against the Cowboys during the 2000 season.