Kevin Doyle had headed in an equaliser after Dorian Dervite had opened the scoring for the Addicks but on-loan Obika struck in added time for the home side.
After watching his side increase their haul to 14 points from the last 18 available, Powell said: "On the balance of chances we deserved the win.
"They had two, the Karl Henry shot and the goal but apart from a few crosses our keeper has not and a lot to do.
"We had the better of the chances and these lads never give up and they dug in again.
"The play-offs are tantalisingly close but it is only a very slim chance. We will still go for it."
As to the contribution of Obika, who is on loan from Tottenham, Powell added: "He has been top class since he came into the dressing room.
"He is good finisher, when he doesn't start he wants to be involved, he always gets chances, which is a good trait for a striker.
"On top of that Jonathan is a good character and deserves hero status for the day."