Stephen Hunt pounced on the loose ball after Paul Robinson saved Leroy Lita's shot in the 78th minute to earn Royals a replay.
Hunt had earlier delivered a free-kick that Robinson carried over his own line for 1-0 before Dimitar Berbatov struck twice - the second from the penalty spot - to put us 2-1 up.
We missed a hatful of chances both before and after Berbatov's double and were made to pay when Hunt struck.
Coppell said: "We got some lucky breaks but when we got a handle on the way we were playing, we made it difficult for them. It was never going to be easy for them.
"I thought we'd get a chance to snatch it and we got some good crosses in.
"But they are good players and for us to come back, they showed me in the best possible way - not through articles in the newspapers - that they have a commitment and want to play a full part in the season.
"In many ways you don't want another game but we are not going to be physically tested with the workload - it is well within us.
"An extra game is no big deal for us. We'll have to have a different game plan at home, we'll have to take the game to them more."
Reading boss Steve Coppell was more than happy to take our FA Cup third round tie back to the Madejski Stadium after it ended 2-2 at the Lane.