The Bluebirds were pegged back by Reading even though the visitors played with a man less for an hour, following Andre Bikey's controversial dismissal.
Wayne Routledge put Cardiff ahead in the 10th minute only for Kevin Doyle to equalise six minutes later.
Bikey received his marching orders in the 30th minute after clashing with Routledge and the 10 men fell behind when Ross McCormack slotted home a 40th-minute penalty after Marcus Hahnemann had tangled with Michael Chopra.
Five minutes after the break substitute Brynjar Gunnarson volleyed in a Stephen Hunt cross and it was Cardiff pushed back on the defensive as Reading went looking for the winner.
"I was very happy to get a point and never question the character of the team," said Royals manager Coppell.
"But I wasn't happy with the penalty or the red card. I am thankful to Marcus Hahnemann for keeping us in the game.
"It looked to me as though Andre Bikey had won his header and he insists that he did nothing wrong. The referee told me he had thrown a punch but I can't see how he could do that when jumping for the ball.
"Under those circumstances it was a terrific point."
The Bluebirds deserved their interval lead as they passed the ball around swiftly and had Reading on the back foot for much of the time, but it was a different story after the interval.
Once Coppell's man had equalised they took control and looked the most likely side to go on to victory.
"Some of our football in the first half was superb but then we lost patience," said Cardiff boss Dave Jones.
"You have to pull defenders out of position and not lump long balls up to them. We switched off at our own corner and let them break for the first goal and then a lack of concentration cost us the second.
"We fell into the trap of trying to force the issue but I am not too disappointed because of the quality of football we played.
"Reading were a dangerous side even with 10 men and we had to make sure we weren't caught on the break."