Van Persie has revealed on his official website he will not extend his contract, which runs out at the end of the 2012-13 season.
While Wenger has already brought in Lukas Podolski and Oliver Giroud to boost his forward options, Smith is unconvinced they can match Van Persie's influence.
"He's got a lot of hard thinking to do now, Arsene Wenger," he said.
"He's brought in Giroud and Podolski but can they replace the 37 goals he got last season? They are going to have to for Arsenal just to stand still let alone move forward.
"It's a double blow for Arsenal because they've also lost a captain, and a good captain too.
"It's going to be very difficult to make up the points they trailed Manchester City last season.
"I'm not saying, though, that they've got no chance at all."