United travelled to Anfield on an 11-match unbeaten streak but suffered the club's worst defeat since losing 7-0 to Wolverhampton Wanderers in 1931, with some former players saying Fernandes should lose the captaincy for his petulant performance.
When asked if Fernandes would continue to lead the side when needed, Ten Hag on Wednesday told reporters, "Yes, definitely".
"I think he is playing a brilliant season and he has played a big role in us being where we are," the Dutch manager added, speaking ahead of Thursday's last 16 first-leg clash at Old Trafford.
"He's giving energy to the team, running a lot with intensity, in the right way. He's pointing and coaching players, he's an inspiration for the whole team.
"No one is perfect, everyone makes mistakes. I'm really happy to have Bruno Fernandes in my team and I'm happy with him as our captain with Harry not on the pitch."
United striker Marcus Rashford (25) also expressed support for Fernandes, saying the Portuguese international is "the perfect player to play with".
"He's been a good leader for us, even when he's not captain, which is always a good sign," Rashford told reporters.
"He's helped other players become better leaders and the reality is that we can't be an organised team in terms of just one leader being captain.
"He's done a lot for us. I don't have anything negative to say about Bruno. As the manager said, nobody is perfect. I support him and I'm 100% behind him."
Ten Hag expects reset
Ten Hag called on his players to reset and bounce back when they face Betis, who are fifth in the LaLiga standings on 41 points and are unbeaten in their last four games - including a 0-0 draw with Real Madrid.
"(The coach and players) are in the same boat, we do it together. We win and lose together. We made a mess on Sunday and we have to deal with that," Ten Hag said.
"(The defeat) had a lot of lessons in it and it can help us in the future. We were really below average, especially mentality-wise.
"We want to win trophies and you have to act different. After Sunday, we got a big lesson, we take it and we have to move on, look forward. Use all the energy and focus on the next game."
Ten Hag's side will be without Anthony Martial (27) and Marcel Sabitzer (28) for Thursday's game, while Donny van de Beek (25) (knee) and Christian Eriksen (31) (ankle) are long-term absentees.
"We have a strong programme," Ten Hag told MUTV in an interview published on Wednesday. "But I think we are quite good."
