The visitors - 17 places lower than leaders United in the Premier League - were blown away in the opening 10 minutes but kept it to 0-0 at half-time before conceding to Nani and Javier Hernandez.
Reading set up a thrilling last few minutes with a late goal by Jobi McAnuff, before Adam Le Fondre came close to a last-minute equaliser.
McDermott said: "Playing United you can easily lose 4-0 but when we got it back to 2-1 and almost scored... well, it was just terrific.
"To come here and perform as well as we did will be good for us going into the last games of the season. United got frustrated but they've got top quality players.
"It makes you think when they can bring on players like Robin van Persie as well. When he was warming up I did speak to him and told him to sit down!
"Credit to our players though. We're disappointed but we were playing against the champions elect. They were very good at times but I'm just delighted at what we did.
"It is the first time I have managed here and it was good for me personally
and my players to come here. We have to come back here in the league and will know a bit more about what to expect.
"We really wanted to put on a performance for our fans and we have done that. We've enjoyed the night but not the result. My keeper Adam Federici made some great saves and you need a few decisions to go in your favour.
"It was a good game for entertainment but now we have to move on and we look forward to Saturday."
The Hoops are third from bottom and are at home to Wigan - one place below them - at the weekend.