"It was important we went through and we did. And even though it was 1-0 I felt fairly comfortable.
"The back four again were superb, along with my goalkeeper so Stevenage didn't give us too many worrying times."
Danny Williams' looping header late in the first half proved enough to take Wrexham into the second round draw.
The goal came from the unlikely source of a Steve Evans cross, and Smith singled out the centre-back for special praise.
"He can play," said Smith. "He's not just a big centre-half who can head it and kick it.
"The fitter he's getting and the more he's getting used to the game, we're seeing more of that side of his game."