Vadaine Oliver's brace in extra time earned the Imps their win after Richard Taundry had struck an 81st-minute equaliser for the hosts.
With the Saddlers now without a win in 11 games, Smith has urged his players to force a change in fortunes and rediscover their impressive early-season form.
He said: "I have told the players not to feel sorry for themselves.
"At the moment, the players are lacking a bit of confidence. I need to help them, but they also need to help themselves.
"We need to turn it around. We have fallen short. I thought we should have won this game."