Fernandes, though, has hit back by insisting "everyone is happy" with the way he leads the squad.
"Obviously you don't like to be criticised, everyone's the same, but at the same time I have to do what I think is the best for my team," Fernandes told a news conference on Tuesday.
"Probably I am not always right but in my head at the moment it is the right choice, so I do it.
"My focus is on the team, the staff, everyone who works with me day by day. I think they are pretty happy with me, the way I am is the same since I arrived at the club, it has not changed since being captain.
"I don't think it has to change. I am really open with everyone so no one until now has had a problem with me, so I think I should keep it like that, everyone is pretty happy with my leadership."
Fernandes, who arrived at United from Sporting Lisbon in January 2020, was made captain in the summer after Ten Hag decided to replace Harry Maguire. The Portugal midfielder has often come in for criticism even before taking the armband, and he believes it's partly down to how well he started at Old Trafford.
He scored 28 goals in his first full season and although he's been productive in front of goal since -- he scored 14 times in all competitions last season -- the 29-year-old has not come close to matching that tally.
"In the beginning, everything was perfect, because when you arrive in the first game, if you do something different than anyone else is doing, it's going be all flowers," Fernandes added.
"But after that I understand the tough part is always coming, because when the result is not coming, when the performances are not what everyone expects to be, because the expectations are always higher and higher.
"I know since I arrived at the club my numbers made myself a target so not keeping the same numbers on goals and assists is sometimes a problem for me. Now it is the captaincy, there is always going to be something."