Smith's 10-man team halted the Cherries' 15-game unbeaten league run and completed the double over the south coast club after a 2-1 victory at Dean Court back in September.
"Bearing in mind how well Bournemouth are doing and the players they have and their spending power, it was a great win for us," said Smith. "They are a good team with good players and will win a lot of games, but I thought we were excellent."
Smith, whose team ran up their fourth successive win and closed in on the League One play-off zone, said the victory rewarded the army of volunteers and club employees - including chairman Jeff Bonser - who cleared snow off the pitch to help get the game on.
He added: "Three points was no more than we deserved, but first of all I would like to give credit to all the people who helped get this game on. It was a fantastic effort."
A 27th-minute strike by Sam Mantom and a Will Grigg penalty on the stroke of half-time gave Walsall a 2-0 advantage.
Brett Pitman pulled a goal back with a header four minutes into the second half and Wes Thomas hit the crossbar for the Cherries before Saddlers striker Febian Brandy was sent off for a second bookable offence after 72 minutes to give Bournemouth a great chance of saving the game.
But a bizarre incident in the 79th minute, when Eunan O'Kane picked the ball up in the area mistakenly thinking Walsall had been awarded a free-kick, handed the home side a second penalty which Grigg duly dispatched for his 10th goal of the season.