Plymouth led twice thanks to goals from Paul Gallagher and Jamie Mackie, but on both occasions promotion contenders Reading fought back, with Alex Pearce and Jimmy Kebe on target.
Coppell said: "I have a sense of relief and disappointment. At 2-1 down I thought this could be one of those games where despite playing a strong part in the game we were going to get nothing.
"At 2-2 I thought there was only going to be one winner.
"I thought we were forceful, as we had been for most of the game.
"In a way I was pleased with a point but a little bit disappointed we did not edge the three.
"You ask your players to give and my players gave today."
Plymouth forward Mackie had set the game alight with a brilliant 25-yard strike on the run after racing from the halfway line, giving diving goalkeeper Adam Federici little chance as the home side went 2-1 up in the 56th minute.
"We got rattled for a couple of minutes after the second goal," Coppell admitted.
"Huge compliment to Mackie for scoring because it's a massively difficult pitch to run with the ball, full stop, and then to run and smash it the way he did. It was a terrific goal.
"But then we got our composure back, played with a real tempo and went from there."
Midfielder Kebe finished clinically for the fourth goal of the game, slotting the ball between goalkeeper Romain Larrieu's outstretched legs after latching on to a through-ball from Marek Matejovsky.
That goal came with 10 minutes left, and neither side could muster a winning goal.
The result means the Royals return from trips to Sheffield Wednesday and Plymouth with four points.
Plymouth boss Paul Sturrock, whose lowly side are now unbeaten in four games, saw his match plans affected by injury and was satisfied with the outcome.
He said: "We had to take off Craig Cathcart with a groin injury midway through the first half and re-organise, and then at half-time Gallagher's hamstring tightened up and we did not want to risk him with a game around the corner at Swansea on Tuesday.
"All things considered with those two off, and changes needing to be made, we did very well.
"If you had said to me that we would be four unbeaten after playing three of the top sides - Sheffield United, Wolves and now Reading - I would have taken it.
"Now the work starts again in building on it with two away games in the next week, at Swansea and then Norwich. We are not out of the mire yet but we are certainly better off than we were a few weeks ago."