Turner claimed Norwich deserved better than a 1-1 draw.
"We were applying lots of pressure throughout the whole game," Turner said on Sky Sports 2.
"We felt comfortable, made one mistake for the goal which was disappointing, but after that I felt we dominated and we're disappointed we've not picked up three points."
On the Villa goal, Turner added: "It's disappointing from our point of view as that was the only real thing they created, but the team showed character."
Wes Hoolahan also felt the Canaries warranted the win, saying: "We dominated it and we were unlucky not to get three points."