Arsenal were beaten on penalties after the scores finished 1-1 following extra-time with Bayindir denying Kai Havertz in the shootout. He also saved Martin Odegaard's spotkick in normal time.
Fernandes, who put United ahead in the second-half, said: "It's a big moment for him, the first penalty and another save here and we are really happy for him.
"It's tough to be second goalkeeper, he came here to play, whenever he gets his chance he's top class for us, he's top class in training, he's always available for everyone and he truly deserves this moment.
"I know we want to celebrate and everything but our focus is now Southampton, that is when we have to back it up. The big games against Liverpool, Arsenal, everyone steps up because it's a big game.
"You want to be in these kinds of games, you want to be involved, you want to be the best but we have to do it in Old Trafford with these fans again. We have to give it back for the club. We need to do it every week, every game."