The Portuguese International hit his kick over the bar in stoppage time at the end of Saturday’s 1-0 Premier League home defeat.
Kortney Hause had put Villa ahead in the 88th minute at Old Trafford on Saturday.
But then handballed inside his own area, and referee Mike Dean awarded United their first penalty of the season.
Boss Ole Gunnar Solskjaer had said before the match that his team were not getting penalties when they should be..
Fernandes tweeted:
“I once again took the responsibility given to me almost since [the day] I joined United.
And I will take it again without any fear or dread whenever called upon.”
Read Also: Today’s Transfer Headlines: Ramsey, Ronaldo,Leno, Kulusevski, Kante, Chiesa, Soyuncu
He added.
“Thank you for all your support after the final whistle! Hearing you chant my name in the stadium was very emotional.
“I will come back stronger for me, because these are the standards I hold myself to.”
There had been talk in the season build-up as to who would be United’s penalty taker after they signed Cristiano Ronaldo.
But even with his miss on Saturday, Fernandes still holds a better penalty record at club level.
He has a 90.7% success rate after converting 39 of 43 club spot-kicks.
While his Portugal team-mate Ronaldo has a rate of 85% after scoring 125 from 147 penalties.
The defeat ended United’s unbeaten league run and came three days after they were knocked out of the Carabao Cup by West Ham.
A victory over Villa would have seen them top the league table.
After Chelsea lost to Manchester City and Liverpool drew at Brentford.
