Snodgrass had entered the final six months of his West Ham contract at the turn of the year, and was sold to West Brom for a nominal fee earlier in January.
West Brom manager Sam Allardyce confirmed before Tuesday's game that with the two clubs scheduled to face each other in the same month as Snodgrass switched sides, an "agreement" was made that Snodgrass would not feature for the Baggies.
However, any such agreement would appear to conflict with Premier League regulations which state that "no club shall enter into a contract which enables any other party to that contract to acquire the ability materially to influence its policies or the performance of its teams in league matches."
While the Premier League rules outlaw any formal agreement, Standard Sport understands it was never committed to writing.
Allardyce had explained before the match to BT Sport: "That was an agreement between the clubs that this game he would not be allowed to play. We could only get the deal done with that agreement."
After the match, Allardyce added: "I’m not going to answer that. If the Premier League want to know that they can contact us privately and we’ll tell them.
"It’s up to the Premier League to let us know what and if we’ve done anything wrong and then I’ll answer whatever questions they decide to ask me. It’s not my big worry at the moment though, what the Premier League do or don’t think."
Moyes said: "I don’t think it is any of my business. I am not sure it is any of yours, to be honest. The pl have to do what they have to do.
"Robert snodgrass is a very good player, we will miss him a lot. We sent him with our best wishes, we did not take any fee for him because we have so much respect for him and what he has done here."