The Royals prevailed thanks to striker Leroy Lita's extra-time goal, but that only told half the story of a 1-0 victory.
But when Lita, making his first start of the season, nudged home Dave Kitson's cross there was no way back for the home side, whose poor finishing ultimately cost them dear.
A relieved Coppell said: "We wanted to be through to the next round and I think that showed tonight.
"We had a desire to be in the next round - we wanted to get through.
Coppell labelled the second yellow card brandished by referee Kevin Friend to Sodje as "outrageous" but also paid tribute to Lita and Kitson.
Coppell added: "They both did terrifically well and you like healthy competition in all positions."