Ricketts, who has dropped down the divisions since his days at Bolton, gave Walsall a perfect start with a tenth minute goal.
It was a simple close-range header from a Daniel Fox cross, but it was an accurate swerving shot from substitute Ishmel Demontagnac which sealed the match for the Saddlers.
Shrewsbury again struggled to recapture their early-season form. Their lightweight attack could make little impact and manager Gary Peters now faces a problem of lifting his mid-table side.
They did come to life for a short spell at the start of the second half following a low key first half. They put Walsall under considerable pressure when Stuart Nicholson went close to an equaliser.
He forced Clayton Ince to make a fine save and minutes later the Walsall keeper foiled another Town attempt when he finger-tipped away a Steve Leslie cross as both Marc Pugh and Nicholson closed in to apply the finishing touch.
Walsall weathered the storm and a timely introduction of Demontagnac settled the tie.
The youngster, who grabbed a spectacular equaliser at Brighton in the previous game, repeated the feat with a long-range swerving shot.
Goalkeeper Glyn Garner seemed to have the shot covered, but the wet ball embarrassingly slithered through his hands and into the net.
The goal effectively killed off Shrewsbury's hopes of a comeback as the Saddlers coasted into the second round to the relief of manager Richard Money.
Money, however, had his head in his hands when Demontagnac collected a Tommy Mooney pass and, with only Garner to beat, blasted his shot over the bar.