Fernandes was speaking after his hat-trick performance in their Europa League win against Real Sociedad.
The Portugal midfielder said on TNT Sports afterwards: "‘It's not nice to hear certain things obviously. I don't think any player likes to hear criticism or things that are talked about to you, that you're not good enough or you're overpaid or whatever.
"Everyone has their own contract. The club agrees to do the contracts at the time you come here or at the time you do a new contract and it's about yourself proving that you can be important for the club."
Fernandes also addressed criticism from United legend Roy Keane over his leadership skills.
"Everyone has an opinion and that’s fine. Roy Keane was an amazing captain for the club - one of the best as everyone says.
"He's massively respected and has all my respect. He has to give his opinion in a programme and that is what he thinks about me. What I’m doing on the pitch is to try to change his mind or try to do something that he probably sees as a good thing.
"Obviously, I do it in my own way. I don't want to copy anyone. I try to be the best captain that I can for my team-mates. I try to help everyone in the best way I can and the best way I know. I have a lot of things to improve, not only as a captain but as a player, a person, as a human being and that's fine.
"Criticism is going to be always a part and it's going to make me grow and understand that there's still a long way to go."
Fernandes also reacted to claims from pundits last week that he should leave United as he deserves better than the team is delivering.
"No, I deserve the same as my team-mates. I'm in the same boat as them. If I haven't given everything to the club yet, or more to the club - it's because I don't deserve it and that's it," he said.
"It doesn't matter how much you do - how much you score, how much you assist - that doesn't change anything. It's about the team, it's about the club to succeed. Obviously, I want to win trophies. I'm not stupid. I want to be in the biggest competitions, I want to fight for the big trophies.
"That's what I said to the club. That's what the club said to me that they want to do. Then it's about the players going on the pitch and the club to do the investments to bring players, take players or whatever they want to do.
"It's not my part to say who's good to come - that has to be the manager and the board. They have to decide. I just want to do everything I can to help the club succeed."
Fernandes then revealed how he considered his options before committing to a new contract last year.
"I sat with the club because I had an offer to leave and we talked about the possibility of me leaving the club or staying. They said what they wanted from me. I just asked if they saw me as part of the future of the club or not.
"I spoke at the time with (Erik) Ten Hag also. He was very clear and the club were very clear with me, that they thought I would be a big part of this rebuild. I heard what they had to tell me. I thought that we could be successful."