Boro's early exit from the FA Cup left them without a game last weekend, and Smith felt it showed against the bottom club.
Marcus Haber's strike put them ahead before the break and Lukas Akins made sure with a second-half penalty as Stevenage climbed back into the play-off zone with their seventh away success of the season.
"It took an awful lot of effort, determination and a couple of good goals, more importantly scored at important times, to get us through," said Smith.
"I was very pleased to go in 1-0 at half-time because after two weeks without a game the group just looked a little rusty and edgy.
"The quality wasn't quite what we all expected and know that we are capable of, so 1-0 at half time was great news."
- Sports & Recreation
- Marcus Haber