A fifth-minute goal from Kalifa Cisse and a header from Kevin Doyle a minute before the break earned the Royals a 2-0 win and strengthened their hold on third place, keeping them a point behind second-placed Birmingham.
United, though, came out fighting for the second half and only a combination of decent goalkeeping from Marcus Hahnemann, last-ditch defending and wayward finishing stopped them launching a fightback.
"I think at half-time we were in a good position but it's a position we have been in a number of times this season and managed on occasions to waste opportunities," said Coppell.
"There was a real determination in the dressing room at half-time to protect what we had and I thought we did a decent job of doing that. It was a good all-round performance, not dependent on any one thing.
"In the first half I thought we played particularly well. I thought we had a real pace to our game, a real edge.
"All in all I thought we played some really good football in first 45 minutes."
Republic of Ireland international Doyle was a thorn in the side of the United defence, particularly in the first half, setting up the opener for Cisse with a low cross after cutting into the area and then heading home his fifth goal in three games to double the lead.
Coppell praised the fine form of the striker, who sits at the top of the Championship scoring charts and signed a contract extension tying him to the club until 2011 last week.
He added: "Kevin is an excellent player. It is the responsibility of good players to produce. Sometimes a player does not develop but I would like to think that Kevin can accept that responsibility and is thriving on the situation."
United offered precious little going forward in the first half, but a double change at the break, with Billy Sharp and Greg Halford replacing Stephen Quinn and Matthew Spring, seemed to spark them into life.
James Beattie, who like Doyle came into the game with four goals in his last two games, made a darting near-post run to get on the end of Halford's low cross, but Marcus Hahnemann got down well to save.
Beattie was also denied by a post when he got on the end of Sharp's cross and saw a header fly over the crossbar late on, while Sharp had the hosts' clearest chance only to be denied by a smothering save from Hahnemann when through one on one with the goalkeeper.
United boss Kevin Blackwell admitted his side were always up against it after conceding so early on, but felt they had enough chances after the break to get back into the game.
He said: "We didn't start bright enough. We showed too much respect to Reading - why I don't know because we have been playing well.
"You can't give a club like Reading two goals like we did, but saying that we created some chances and have not taken them.
"We took the game to them in the second half and they only really threatened on the break.
"Hahnemann has made crucial saves and every time the ball went into their box it seemed the referee blew (his whistle)."