Lee, the son of former Hammers and Newcastle United midfielder Rob Lee, replaced Ricardo Vaz Te with 78 minutes on the clock at Old Trafford.
"I'm over the moon and had a brilliant night. It would have been great at Upton Park but the next best thing is the Theatre of Dreams at Old Trafford, so I'm delighted the gaffer decided to chuck me on," Lee confirmed to whufc.com. "It's unfortunate about the result but I'm still happy from a personal point of view.
"Obviously it would have been great if one chance had dropped to me but I was just happy to be out there playing alongside the likes of Wayne Rooney, so I thought it was brilliant.
"It has been going really well. I was top scorer for the youth team last season and I've pushed on to the Development Squad this year, so hopefully I can keep pushing on and push for a place on the bench for the first team."