They were frustrated by a well-organised Palace outfit and finished the game a man down after defender Liam Rosenior was sent off.
Coppell was unable to secure back-to-back wins in the week he celebrated his 1,000th game as a manager - more than half of which were in charge of Palace - but promised his side would come back strongly after the international break.
"They had more pressure than us and when we went down to 10 men it looked like that pressure might tell," said Coppell.
"But we defended well and it was good to get a point given the circumstances.
"All the teams are feeling it, we've had seven games in 21 days and it takes its toll.
"It's nice now to have a break and everyone in the division can set themselves up for the closing month of the season.
"We are one of the teams with a lot to play for and a lot to look forward to. We have an opportunity to show our nerve and our ability and try to get something for it."
Rosenior saw red for chopping down Palace youngster Victor Moses on the edge of the penalty area with 18 minutes remaining, and Coppell had no complaints about referee Andy D'Urso's decision.
But he did feel the official missed a decent penalty shout for the visitors after Jose Fonte clipped Dave Kitson.
"Andy D'Urso is one of those referees who an awful lot seems to happen around him," Coppell added.
"I thought we had a great shout for a penalty in the first half. The sending off, we can't do anything about it, he thought it was right and we'll accept it."
Nathaniel Clyne and Moses tested Reading goalkeeper Marcus Hahnemann with stinging drives either side of the interval and manager Neil Warnock is bracing himself for summer bids from Premier League sides for the talented teens.
"They are two exceptional players," Warnock said. "I think all the big boys will be queueing up for them soon.
"I can see the top four taking them. Hopefully we'll get another season out of them but it wouldn't surprise me if we get an offer we can't turn down in the summer."