After United's 3-0 derby defeat against Manchester City, club legend Roy Keane said he would take the armband off the 29-year-old.
Fernandes' attitude on the pitch has often been criticised and some fans did question the decision to make him captain.
However, he emerged as United's hero on Saturday with a late winner away at Fulham in what could prove to be a crucial 1-0 win.
And following the victory, Ten Hag issued his response to claims that he should relinquish the Portuguese star of his captaincy duties.
"I don't understand it," he told TNT Sports. "Everyone has mistakes and no one is perfect but he's doing a lot of things very good.
READ MORE ON MAN UNITED
McTominay responds to five-word Man United banner amid 'relentless' fan support
Fernandes eases pressure on Ten Hag with last-gasp heroics for Man United at Fulham
"He's showed every time as a captain he's an example, you've seen today how he's working, how he's pressing and in the end he scored the goal. So, he's massively important for us."
Ten Hag also had a brief clash with fellow Man United legend Rio Ferdinand in a tense interview.
United were underwhelming yet again despite the late winner and Ferdinand asked when the manager will inspire a consistent style of play.
Ferdinand said: "I saw some comments from you before the game about the playing style.
Most read in Football
Fulham star leaves pitch in tears and consoled by Maguire during Man United clash
Leeds fans mock Man United and Ten Hag and Old Trafford with new chant
Marcus Rashford not included in Manchester United squad to face Fulham
Fulham 0-1 Man United LIVE: Fernandes scores injury-time winning goal to rescue Ten Hag
"How long before we see a team where you say, 'This is how I want to play'. At the moment, consistently, we're not seeing that.
"You would probably agree."
Ade Oladipo claims Marcus Rashford's poor form is down to him and not Manchester United boss Erik Ten Hag
Ten Hag responded: "With all due respect, didn't we see it last season?"
And Ferdinand interjected: "Last season we saw it, this season we haven't."
Ten Hag responded: "No - but anyone knows why. We have so many injuries.
"Every time you have to make changes and the routines are not there. We have to be more pragmatic.
"It's not an excuse. Even if the players are not available for the same roles, the quality is there.
"They are good players but they have to play games in the same line-up for the routines to be there and we can play better."