The Poland goalkeeper was a late withdrawal for the 2-1 loss.
Moyes said, "Lukasz Fabianski was injured today. Unfortunately, somebody stood on his arm in training as he made a save.
"It was an accidental collision and I don't think it's too bad.
"Darren Randolph has been out in recent weeks with a bit of a thigh strain. He's been back in training for a week or two but I think he felt the effects of his thigh again.
"Thankfully, we got him through to the end of the game. We were ready to make a change, but we found a way for him not to have to take the kicks.
"Hopefully he'll get over it and we'll also get Lukasz back."