Simon Ferry opened the scoring after just 57 seconds when he lashed home a cross from Gary Roberts, before Matt Ritchie made sure of the points with a low drive after 62 minutes.
Walsall’s best effort came from a Jamie Paterson free-kick which Swindon keeper Wes Foderingham turned round a post at full stretch.
“Swindon are as good a team as we have played against in terms of physicality and the quality of their players. They are right up there,” Smith said.
“We showed a lot of endeavour but were on the wrong side of the result. Swindon have spent a lot of money but this football club (Walsall) have good people who want to work here.
“A lot of clubs out there go into administration and have transfer embargoes, but this club runs a steady ship and will continue to do so.”
Real Madrid superstar Cristiano Ronaldo took the opportunity to slam his critics as he is named best Portuguese player of 2017 on Monday.
Liverpool defender Virgil van Dijk reckons that he can do even better despite an immediate upturn in the defensive form of Jurgen Klopp's side since his arrival.