Nineteen-year-old Drameh has been continually impressing for United's under-23s and the England youth international was handed his first minutes for the first team when starting Tuesday evening's cup clash at the Emirates.
Marcelo Bielsa's Whites created several good chances in the first half but fell a goal down in the 55th minute when Calum Chambers headed home a corner just 23 seconds after coming on for the injured Ben White.
Fourteen minutes later, United conceded for a second time as former Whites loanee Eddie Nketiah seized upon Liam Cooper's short headed back pass and clipped the ball over Illan Meslier before converting from a tight angle.
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Drameh played the full duration of the contest but admitted he was left with mixed emotions given the result.
"It's sort of bittersweet," said the teenager to the BBC.
"First of all I would just like to thank God and thank the closest ones near to me and thank my family as well for getting me to this moment.
"It was a really tough game against a really tough Arsenal side.
"They made it tough for us on the counters and stuff like that.
"It was really bittersweet but I was really happy to make my debut.
"I think the second goal kills us a bit because when it's 1-0 we can get a goal back and we are still in it.
"But to concede one goal and then to concede another one, it just makes it tough for us and digs our own grave really so we can't back into the game."
Asked when he discovered he would be starting and how he was informed by United's head coach, Drameh said: "I found out at midday.
"We had a meeting and he brought me in with his translator and he just showed me a few clips of how I have been previously playing.
"After that he told me I am starting and I just had to keep my composure until after the meeting then I just told the people who are closest to me and they were buzzing for me.
"Throughout the day my heart was just really beating.
"It's been really different to any other game I have played in.
"Usually I am more kind of relaxed but obviously it's my first team debut.
"I was nervous but excited as well."
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Thank you Laura Collins