Will Grigg got his first from the penalty spot after just three minutes and added two more second-half strikes as Carlisle were handed a lesson in pace and accurate passing by the Saddlers, who won for the ninth time in their last 13 games.
After the 3-0 win at Brunton Park in League One on Tuesday night, Smith said: "I've always seen Will's qualities and he is coming through now. He ran his socks off and not many centre-halves will want to play against him.
"He is a nuisance who does a bit of everything. Will gets the accolades for his hat-trick, but I felt it was a full team effort from the keeper all the way through the side."
Smith added: "I'm really proud of them. With 52 points, it's nose-bleed time, but I haven't got time to think about the play-offs.
"We just take a game at a time and keep moving on. We were phenomenal and could have had a few more.
"I've got every admiration for Greg Abbott and what he's done on a tight budget and a performance like that is really pleasing.
"I thought the reception we got from the Carlisle fans was fantastic."