It was Charlton's first win of 2014, and came after they almost went out to League Two Oxford United at The Valley last week. They trailed 2-0 at half-time but battled back to 2-2 with Kermorgant equalising late on.
At the Kassam Stadium they bossed the replay once Kermorgant and Green struck twice in three minutes near the end of the first half.
And Powell said: "Considering what we went through in the first game, I was very pleased with how we did in this one.
"Even though we had had a long trip to Middlesbrough last Saturday I thought the players put in a sterling effort.
"The goals came at the right time and I thought we were quite clinical. I'm pleased with all aspects of our play and for our fans as well."
Powell is now hoping that the victory - only the Addicks' second win in 11 games - will revitalise them and boost their bid to beat the drop in the Championship.
He said: "We do need some momentum and to instill some confidence in the side, and we'll gain that tonight.
"Yann is our talisman in some respects and I was thinking of not playing him here. But he is so important to us.
"Simon Church, who is desperately chasing a goal, was very selfless for the second goal. He could have gone for goal but did the professional thing and squared it."
- Sports & Recreation
- Yann Kermorgant