Fabio Borini raised eyebrows after hammering home Sunderland's late equaliser against West Ham, running towards the dug-out in what seemed like a pointed response to his exclusion from the first XI.
The Italian had reacted in a similar manner last season, after scoring against Crystal Palace late in the game to salvage a point for Sam Allardyce.
A sense of unrest was heightened post-match when Borini hinted at his frustration at not playing alongside last season's successful forward line, as well as saying the squad was not as 'united' as in previous seasons. He did, however, clarify that remark by saying that injuries were the primary reason for that.
His manager has insisted that unhappy players are an inevitable part of football but did feel the celebration could have been more constructive.
Moyes said: "The first thing I would say is that I think it would have been good if he ran into the net, got the ball out and ran to the centre circle so we could kick off and try and get the three points, I think that would be the thing to do for the team.
"As for the comments, look, I work with players all the time, there will always be some players who ultimately aren’t happy."
Moyes insisted that his squad showed a reaction to their plight against West Ham United and is looking for them to replicate that commitment in the coming games.
A poor set of results from the Black Cats perspective at the weekend has left the table looking bleaker than ever, and Moyes has spoken of his anguish at the predicament.
He said: "We want players to fight for the jersey, showing commitment in every game, that’s what we’re looking for.
"We’re gutted at the position is in, if any supporter feels it’s just them, we’re devastated by the position we’re in, but we’re at it, training hard, we want people who will show it and fight. I want us to show that we’re there and I thought the players showed it big style against West Ham."