The visitors looked like paying for their failure to make that superiority count when Adam teed up fellow substitute Michael Kightly to tuck home a leveller late on.
But little could be done to keep out Matt Lowton's long-range volley and there were no complaints about the final result.
Adam, 27, who joined Stoke from Liverpool last August, said: "We shot ourselves in the foot again.
"We got back to 1-1 and tried to go for the game. The way we played a point probably would have been a good result but we have conceded three and it is difficult to take.
"Fair play to Aston Villa. Both teams are under a bit of pressure but the way they played was magnificent.
"I think the goal the lad (Lowton) scored was an incredible strike, you can't take that away from him."