First half goals from Febian Brandy and Will Grigg gave the Saddlers their fourth win in five games since going 16 without a win.
Smith said: "I'm proud of the players.
"We never reached the heights of the last few weeks but on the balance of play I thought we were the better team.
"We looked tired towards the end but we have played five games in 13 days and won four of them, which is a magnificent achievement. We have taken 12 points out of a possible 15 which is not bad at all.
"We were not as fluent as we have been and there were some misplaced passes which gave them hope in the game, but when we got the first goal I think their heads dropped a bit.
"We have been pretty consistent and it was just a case of getting wins, but since getting 'over the line' against Colchester we have done very well."