Manchester United once again failed to hold onto a lead in normal time, conceding a penalty to let Burnley score an equaliser.
Antony scored for the Red Devils to send them up by a goal towards the end of the second half.
The lead barely lasted minutes as Andre Onana gave away a penalty, which Burnley converted.
Christian Eriksen was one of the more average performers in the game, failing to match the tempo of the midfield.
Assessing his own performance, Eriksen told MUTV: "Of course, I still think there's some bits that still could be better today, a few decisions that could have been better and put my team-mate or myself in a better position around the pitch.
"I'm trying to do my best. It hasn't been as much game time, but when you're on it, I think you have to do your best. And that's what I'm trying to do."
Eriksen has played 22 times across competitions this season, appearing mostly off the bench.