Makama, the most impressive player on the field, showed his intent when he crashed a 14th-minute effort off the upright from 12 yards.
The forward was the bright point in a quiet first period and, having set up a long-range Kenny McLean effort, he came close to getting on the end of a Ben Chrisene cross.
Ruairi McConville hooked a shot over the Charlton bar 11 minutes from the break, while Matej Jurasek forced Thomas Kaminski into a good save five minutes later as the Canaries were untroubled in a first period in which the Addicks failed to register a meaningful effort on target.
Norwich brought on Jacob Wright and Tony Springett at half-time to try and add some attacking intent, and the former almost got on the end of an excellent cross by Makama.
But the striker did put his side in front when he controlled a firm Wright pass 12 yards from goal, swivelled and powered home with his right foot.
Oscar Schwartau came close to making it 2-0 10 minutes from the end, but Kaminski did well to palm away his shot from inside the box.
Charlton again failed to trouble their hosts as boss Nathan Jones – in the stands after a third booking – saw his side lose for the sixth time in eight matches.