Paterson hit the first and last in the Saddlers' biggest win of the season which avenged their heaviest defeat, 5-1 at Coventry in November, and they are now unbeaten in 12 games.
Smith said: "I thought Jamie was outstanding. He finished really well and could have had another couple towards the end. Some people had wondered how we would do without Will Grigg."
Asked if it had been his ambition to play for Coventry as a boy, Paterson said: "I was a Coventry fan as a youngster, but my ambition was just to be a professional footballer. Next season they will be a very strong side if they keep their players.
"Our season turned round after the defeat at Coventry. Perhaps that was a kick up the backside and our results turned round."
Coventry had defender Jordan Stewart sent off for his second yellow card on 65 minutes, but they were already two down at the time, and Walsall never let them off the hook.
Paterson opened the scoring in the 33rd minute and notched his 13th of the season to complete the scoring three minutes from the end.
Craig Westcarr hit the second goal from a 53rd-minute penalty and headed the third after Paterson's free-kick had been blocked.