The Daily MAil says the midfielder, 32, stormed down the tunnel and hurled his shirt on the floor after being hauled off during last Saturday's 1-1 draw with Norwich. He was then left on the bench for the 1-0 win over Swansea on Wednesday.
Moyes was unimpressed but has been pleased with the Australian's response in training and may recall him for the Boxing Day trip to Sunderland.
Moyes said: "His reaction to being taken off wasn't great. He's hurting but what's happened has refocused him. Hopefully we will see the benefit."