Zaha, 26, was the subject of a £50million bid from the Gunners in the summer – but the South Londoners refused to sell for less than £75m.
Hodgson said: “Wilf missed training. For two days he didn't turn up.
“The fact he wasn't here was a sign that his head was not where it should have been.
“But the period passed very quickly. He played in our next game.
“It happened to me at Liverpool when Mascherano did it after my first game in charge.
“Then Mascherano went on strike. Refused to play. Didn't play the next two games.
“Wilf never did that. He missed a day or two and he might have given interviews, saying, 'My head is all over the place, I am not happy'.
“But he didn't point-blank refuse to play unless he was sold."