The Addicks struggled to break down a dogged Lions outfit at The Valley and eventually went down to a deflected effort from Scott McDonald.
A response to that effort never looked like coming, with Millwall goalkeeper David Forde untroubled until the closing stages.
Powell concedes that Charlton must raise their standards considerably in the final third if they are to are to remain competitive in the Championship.
He said: "It was a home game and a derby and I wanted us to put the opposition on the back foot but we didn't do that.
"In the first half I really needed more from my players, in respect of creativity.
"Then after the goal we were always chasing the game and although we had one or two situations we couldn't break the deadlock.
"We've got to realise it will be a tough old season for us but we have to believe we can turn it around.
"Millwall were buoyed by their result in the week and they've showed how quickly things can change."