Aston Villa central defender Alpay has apologised to goalkeeper David James after striking him in the face during Saturday's Premiership encounter with Liverpool.
Alpay made his peace with James and Villa manager John Gregory at the club's Bodymoor Heath training ground.
But Gregory has still taken disciplinary action against the Turkish international, although he would not confirm whether this involved a fine.
Alpay lost his cool after his mistake gifted Liverpool their opening goal in a 3-0 success and he then confronted James and landed a blow on the former Liverpool star.
It needed Villa defender Steve Staunton to separate the pair and Alpay was substituted at half-time, although Gregory insisted that was a tactical move.
Gregory said: "The matter has been dealt with. Alpay has apologised to me and David. We all shook hands this morning and will now get on with things.
"There was no big show in front of the other players. We did it privately and the matter is now all over.
"Alpay has been disciplined although I won't say what that involves. It was not the sort of thing I would like to see on the pitch. You can do without that kind of thing.
"But it was a heat of the moment sort of thing and Alpay and James are both passionate about football, and both like to show it at times.
"Although I don't condone Alpay's action, I've got less time for people who just walk way and don't give a monkey's about things. Those two both care a lot about doing well."
James said: "We have made up. I was very disappointed in what happened and you can't forget something like that.
"But I recognise it happened in the heat of the moment. Things were very tense out there."