Reports emerged on Thursday that Luiz had left Ceballos with a bloodied nose after clashing during a training match earlier in the week.
Both players were sent home, after Mikel Arteta had brought a halt to the session when Ceballos was left lying on the floor with a scratch on his face.
"It's just competitive training, that's all we want it to be," Holding told Sky Sports . "We want it to be match-like, you've got to train as if it's a match.
"You want to fight and compete for the ball. If it goes over [and] it can't go over, it can't go over, and it's displaying something that's not part of the game.
"Everything that happened was just competitive tackling and just a bit of competitiveness with the boys, which I think is not a problem at all."