The United winger joined Cardiff on loan last month after being unable to cement a first-team place under Moyes following his move from Crystal Palace.
The 21-year-old published a picture of him receiving instructions from Cardiff boss Ole Gunnar Solskjaer, and he added a caption which read: "Nothing like someone who believes in you..."
Many observers believed the comment to be a thinly-veiled attack on Moyes for frequently overlooking the England international, who made only four appearances for United before being offloaded to Cardiff.
But after deleting the image, Zaha insisted his comment was in praise of Solskjaer and was not intended as an attack on Moyes.
"My picture actually meant Ole Solskjaer has a lot faith for me to do something for Cardiff's current position," Zaha wrote.
"My last Instagram picture was not intended as a dig or indirect at my manager, I have nothing but respect."