James Dunne's scorching volley put Boro in front but former Wales international Paul Parry had the hosts level by the break before Marvin Morgan, on as a late substitute, converted a cross from Jon Taylor to seal victory for the Shrews five minutes from time.
A brilliant stoppage-time save from goalkeeper Chris Weale denied Stevenage skipper Mark Roberts an equaliser.
Boro have now lost four successive games and Smith, disappointed that two strong penalty claims were rejected in the second half, said: "To take the lead again and to lose the game was heartbreaking to say the least.
"I thought we controlled the opening 15 minutes and on possession and territorial advantage we maybe deserved to get a goal and it was a great strike again from James. It was a really positive start to a tough away game.
"I was very disappointed with the equaliser. Shrewsbury had had few moments around our penalty area and the first real chance they've scored. Parry hits a good strike but it should never get to that point.
"We were quite happy moving into the second period and it again showed that we're capable and there's still plenty to play for.
"Really and truly we should have been given the opportunity to go in front but the referee was a big factor in that because it's his decision and choice whether or not the two calls are right. Only on replays will I be able to tell you that."
Smith, admitting his side's run of defeats was a concern, added: "We have to somehow find a result that tips the scales the other way. We've got enough quality in the side to be turning results around in a far better fashion. There's no doubts about it."