Bolton were on course to inflict yet another home defeat on the Addicks as they took a 2-0 lead, but goals from Johnnie Jackson, Dorian Dervite and Yann Kermorgant turned the game around.
The visitors had both Samuel Ricketts and Craig Davies sent off, and Powell was delighted that his side made their advantage count.
He said: "It was some game, but at 2-0 down it wasn't. To be honest, we've done it already once this season, but regardless of the sending off it showed the mental strength of the players.
"To drag themselves up from that, the momentum went in our favour - Johnnie Jackson was immense.
"We took advantage of the first sending off, and the crowd got behind us. They were frustrated but they showed how much they wanted us to win.
"We kept going in that 10-15 minute period in the first half to give ourselves a fighting chance. Our goal gave Bolton food for thought."