Antony is currently on-loan at Betis from United and has managed to rebuild his career after a difficult two years at Old Trafford.
Ten Hag signed him from Ajax and he told ESPN Brasil: "I am very grateful to him.
"He has always helped me in the Netherlands, but also in England, even though I did not get the chances I wanted there. Those are choices of the coach and I do not blame Ten Hag for that at all.
"On the contrary; I am so grateful for everything he has done for me and for all the great conversations."
Antony also had positive words for Betis coach Manuel Pellegrini, adding: "He called me personally when I was in Manchester. That immediately gave me confidence to play my best game.
"He is a great coach and a kind of father to this group."