The Red Devils suffered elimination from the UEFA Champions League with a 2-1 aggregate defeat to the Spanish champions.
Rashford's form has dipped this season and he could not inspire a turnaround for Ralph Rangnick's side when he appeared as a second half substitute with 20 minutes to play.
A video emerged on social media of Rashford angrily confronting some fans outside Old Trafford after the game and he had to be restrained by security.
However, Rashford has denied he used his middle finger during the angry confrontation.
In a message posted on Twitter, Rashford wrote: "A video can paint a thousand words and in this case lead to inaccurate info being shared on social media.
"Guys, for weeks I've been heckled, threatened, questioned and last night my emotion got the better of me. I'm a human being.
"Reading and hearing that stuff about yourself every day, it wears you down. No one is more critical of my performance than me. But what you see in this video lacks context. I had been heckled from the minute I stepped foot outside the ground, abuse not just aimed at my football.
"People were looking for a reaction from me. Phones were at the ready. Of course, I should have walked straight past and ignored it, that's what we're supposed to do right?
"I want to clarify two things. The first being what I actually said to the man throwing abuse at me which [was] 'come over here and say it to my face' (a fact security can back up) and secondly, the fact I used my forefinger to direct the fan to 'come over and say it to my face'. I did not gesture with my middle finger.
"I'm not entitled. This isn't ego. I'm upset. I'm disappointed. And in that moment it was silly but I was being human."
Rashford has made 26 appearances for Manchester United this season, scoring five goals.
