United missed the chance to go top of the Premier League after going down 1-0 at home to Dean Smith’s side at Old Trafford.
Kortney Hause’s 88th minute header ultimately proved to be the winner but the home side were handed a lifeline to at least nick a point when Villa’s goalscorer handled in his own box shortly after.
Fernandes pulled rank over Cristiano Ronaldo to take the penalty but sent his kick over the bar.
This was only the second time Fernandes had missed from the spot in 23 attempts for Manchester United.
"Nobody is more frustrated and disappointed than me for missing the penalty and the consequent defeat," Fernandes wrote via social media.
"I've always assumed my responsibilities and I've always embraced them under pressure in moments like this. Today, I failed. But I took a step forward and faced the challenge with the same ambition and responsibility as when, on the many other occasions, the ball ended up in the net.
"Criticism and contrasting opinions are a big part of football. I've learned to live with it, even using them to drive me on, and I consider it all a very important part of my commitment to never stop trying to improve and to become the best player I can possibly be, for me and the team.
"Today I once again took the responsibility given to me almost since I joined United and I will take it again without any fear or dread whenever called upon.
"The most important thing for me is to win together and I'll always do everything I can to help my team-mates and the club to be the best we can be.
"I'm a player who leaves everything on the pitch, with great desire and commitment. And that's what I'll continue to do.
"Thank you for all your support after the final whistle! Hearing you chanting my name in the stadium was very emotional… I will come back stronger for me, because these are the standards I hold myself to, but most of all for my team-mates and our fans who have always supported us."
