In normal time, Ole Gunnar Solskjaer’s side were held 1-1 in Gdansk by underdogs Villarreal, who triumphed 11-10 on penalties after David De Gea’s spot-kick was saved.
Rashford faced the media after the match and later received a torrent of racist abuse when the United forward opened up his phone.
“At least 70 racial slurs on my social accounts counted so far,” the United forward wrote on Twitter.
“For those working to make me feel any worse than I already do, good luck trying.
“I’m more outraged that one of the abusers that left a mountain of monkey emojis in my DM is a maths teacher with an open profile.
“He teaches children!! And knows that he can freely racially abuse without consequence…”
Rashford also sent a thumbs up emoji to a user who said of the racist abuse: “You deserve it man you are awful.”