The hosts took the lead when Tony Watt connected with Johnnie Jackson's pass to fire the ball past Mark Cousins.
Karlan Ahearne-Grant doubled their lead before Zakarya Bergdich scored on his Charlton debut to make it three.
Christian Doidge's goal gave Dagenham some hope before Reza Ghoochannejhad scored Charlton's fourth.
Dagenham gave Nicholas Hamalainen his debut following his one-month loan from QPR and the young midfielder almost provided the visitors with an early lead, but Nick Pope saved his long-range strike.
Charlton opened the scoring when Jackson played the ball to Watt, who registered his second goal in as many games before 17-year-old Ahearne-Grant scored his first goal for the Addicks.
Watt turned provider as he sent the ball into the box for Bergdich to calmly finish, but Dagenham pulled a goal back after Ashley Chambers set up Doidge to finish.
Substitute Ghoochannejhad gave the hosts their fourth, ensuring that Charlton have now scored four goals in a first-round League Cup tie for the third season in a row.
Charlton Athletic were comfortable winners over Dagenham and Redbridge as they secured their place in the League Cup second round.