Forest dominated possession from the outset and were close to taking the lead in the early stages when Adlene Guedioura's powerful strike crashed against the crossbar.
Charlton's midfield struggled to assert themselves in the contest during the first period with the visitors failing to threaten the Forest defence.
McGugan broke the deadlock in the 17th minute with a curling free kick from long range that left Ben Hamer with no chance.
Johnnie Jackson could have levelled the match but his poor header bounced well wide of the goal.
Despite the hosts controlling the match, Hamer was not troubled in the closing stages of the first period.