The 24-year-old has a single goal and one assist this season, both against League Two team Newport in the FA Cup.
Against Fulham he was left out of the starting line-up as 19-year-old Omari Forson was handed his full debut.
Ten Hag defended his decision even though Forson failed to shine. And he insists his faith in Antony remains strong.
“I brought in Kobbie Mainoo,” Ten Hag said. “Now, after six weeks, the same people who were questioning it are saying he has to go to the England squad.
“Garnacho: what is the manager doing? What is the staff doing? Similar. They need time.
“Omari came on and it’s not easy. We didn’t play our best game but he plays a reasonable game and showed that he can be a player for the future.
“On Antony, I backed him for a long time. I know his abilities. I know from the past he is unstoppable. He’s one of the quickest in the first 10 yards.
“He is resilient, he’s a character and he will fight back and I back him.”
Ten Hag ‘doesn’t care’ about job speculation
In addition to Carragher’s criticism of Ten Hag’s tactics, Neville also suggested the Dutchman’s future at the club was open to question.
Given new minority owner Sir Jim Ratcliffe did not appoint him and results this season have not been good, that is understandable.
However, with a trio of European heavyweights in Barcelona, Liverpool and Bayern Munich already knowing they need new coaches in the summer, Neville feels it is possible a judgement on Ten Hag has already been made.
The former Ajax coach still has another year left on his present United deal and has repeatedly said talks with Ineos representatives have been positive and both sides are “aligned” in their thinking.
“I’m under contract for three seasons, so I don’t care,” he said. “I have many talks with Sir Jim Ratcliffe, also with Sir Dave Brailsford and others in that group, so I know what we are talking about and I have a strong belief and I feel that they believe in me.
“If you talk about one defeat and the manager’s position is in discussion, I think it’s quite opportune after two months without a defeat.”
Ten Hag did almost manage two months without a defeat but January only contained three games, two of which were in the FA Cup against lower league opposition in Wigan and Newport.
A fifth-round tie at Nottingham Forest is a very different matter entirely, but Ten Hag feels the demands are the same.
“It’s normal, we have to win,” he said. “Players have to understand this, managers have to understand this.
“I understand the criticism when we don’t win and that the criticism is coming. Some opinions are true, but many are untrue. What is important is the truth we have in here. It’s our truth.” Eric concluded.