Nicolas Anelka's free-kick gave Wanderers a half-time advantage but Luke Moore deflected in with his chest to leave the match deadlocked.
But Megson, whose appointment this week has been met with anger by sections of the Bolton support, was pleased with his team's showing this afternoon.
"I was happy with the effort," he told Sky Sports 1.
"At times I didn't think we could sustain it, and we weren't as solid as the first half (after the break).
"But it gives us a bit of optimism to go forward."
Megson was left unhappy by Villa's goal, however, when the referee overruled his assistant to award a throw-in to the visitors which led straight to the equaliser.
Asked if the goal upset him, he added: "The nature did. I thought it was our throw-in but the referee overruled the linesman."