Boro have quickly climbed the football pyramid and face Sheffield United in the League One play-offs after coming up from League Two and the Conference in the previous two seasons.
"I think it's a massive achievement for anyone to go through leagues and readapt and rebuild and remain competitive and ultimately successful," Smith told Sky Sports News. "It's a wonderful achievement for any team but I think for a side that has come through amateur, part-time and then into full-time football and quickly go through those divisions is testimony to the guys that are
"They have acquitted themselves incredibly well in League Two and now League One and the nucleus of the side is pretty much the same. And I also think it is testimony to the support they get from around the club and the fans, of course. Everybody is really riding this wave at the same time."
Stevenage drew 2-2 with Sheffield United at the end of April and beat the Blades in the league at home this season. Ahead of the semi-final first leg at the Lamex Stadium, Smith added: "We've actually not lost to the Sheffield sides, which is a terrific record.
"To go to Bramall Lane under the circumstances we were involved in and get a very valuable point was terrific - but perhaps at the time we felt we should have got more from that game - as it gave us control over the last weekend of the season."