Sky Blues substitute Nathan Delfouneso scored the decisive goal and his first for the club since arriving from Aston Villa on loan in January, either side of Callum Wilson's opener and Malvind Benning's equaliser.
It leaves the out-of-sorts Saddlers still five points adrift of sixth-placed Peterborough ahead of Saturday's tough assignment at home to leaders and local rivals Wolves.
"I'm disappointed and amazed we have been beaten in this game," Smith said.
"I thought we were excellent. I just said to the players I'm really proud of the way they played and the way they moved the ball.
"Technically we were excellent. I think for their first goal Febian Brandy got a push in the back and they go up the other end and score.
"We're in a bit of a poor run at the moment where things aren't going our way but the response from the players has been excellent.
"We're pleased that Malvind got the goal but disappointed for the players because they played ever so well, and we're amazed that we've come away with nothing.
"The performance was terrific and despite the result it was a real positive to take from the game."
- Sports & Recreation
- Malvind Benning
- Nathan Delfouneso
- Callum Wilson
- Aston Villa