Millwall didn't allow the home side any time on the ball though, as their pressing game forced the Addicks into a number of mistakes.
Andre Bikey should have headed the hosts in front a minute before the break, but the central defender nodded wide of the mark from Johann Berg Gudmundsson's corner.
Scott McDonald thought that he had given Millwall the lead four minutes into the second half, but the flag had already been raised for offside by the time the attacker had the ball in the back of the net.
Callum Harriott then saw a couple of shots blocked before Gudmundsson drew a fine save from David Forde as the home crowd roared their side on in search of an opener.
Harriott then saw another effort cleared off the line, but Charlton were left to thank Pope, as the goalkeeper denied Jermaine Easter and McDonald's deflected shot in the final 10 minutes.