Fernandes scored from the penalty spot to earn Man United a 1-1 draw with Chelsea in their first Premier League game since Ten Hag was sacked.
The midfielder said he spoke to his former coach following the club's decision and admitted the players were to blame for Ten Hag's departure.
"Whenever you see a coach leaving the team, you have to take some responsibility for yourself, because the team didn't play well," Fernandes told Sky.
"It's easier to get rid of a coach than to get rid of 15 players. I spoke to Ten Hag and apologised to him. I was disappointed that he left and I tried to help him. I didn't score, we didn't score and I feel partly responsible for that.
“It’s not good for anyone at the club when the coach leaves. The team is not in the best form, the results are not the best and he is the one who has to pay for that,” said the Portuguese midfielder.
Since Ten Hag's sacking, United have beaten Leicester City 5-2 in the Carabao Cup and drawn with Chelsea in the Premier League under caretaker manager Ruud van Nistelrooy.
Van Nistelrooy will take charge for two more matches before Ruben Amorim takes charge on 11 November.
Van Nistelrooy admitted it had been a “difficult” week at the club and said the players had had to “look at themselves” after a poor start to the season.
“It’s been a tough week, a roller coaster of emotions. It was sad to see Erik ten Hag leave the team. Then we had to start preparing for Leicester City in front of 75,000 people at Old Trafford. The reaction of the players then and now shows that they have thought about everything,” Van Nistelrooy said.
Van Nistelrooy's long-term future remains unclear after Amorim announced his intention to bring his coaching staff to Old Trafford.
The Dutchman will take charge of Man United against POAK in the Europa League and Leicester in the Premier League in the short term, with Van Nistelrooy remaining at Old Trafford as an assistant manager still unclear.
"I'm open about my future. We will all support Ruben Amorim and help him take Man United to where we want to be.
I myself would like to know him better. Amorim has done a great job in Portugal. He is a young, talented coach and has achieved a lot of success in Portugal," Nistelrooy concluded.
