Smith's side are locked at 0-0 with the Blades after Friday's tense first leg at Broadhall Way, but the former boss of Major League Soccer side Colorado Rapids dismisses any suggestion Stevenage have blown their chances of a third successive promotion.
"We're well and truly in this," said the 43-year-old, who replaced previous boss Graham Westley in January.
"We had a frustrating night and one that I feel saw Sheffield United pay a lot of respect to us.
"They defended very well, they were professional in their approach and when they had the ball, despite not creating many opportunities, they managed possession well.
"They made us work, but it's now 0-0 at half-time. We scored two goals at Bramall Lane two weeks ago so there's no concern in our minds that we can go and get a result."
Stevenage, who have gone from the Blue Square Bet Premier Division to npower League One in three seasons, drew 2-2 with the Blades at Bramall Lane last month and beat them 2-1 in the league at home in November.
Smith admitted he had to lift his players after Friday's stalemate, but added: "That's testimony to how far this group has come. We're fighting for a Wembley place here and this is not going to be easy.
"Whatever side we put out we'll give Sheffield United a fantastic game up there.
"We'll take it as far as we can and if that means penalties, we'll go to penalties."
Sheffield United manager Danny Wilson is hoping striker Richard Cresswell can return to boost a depleted forward line.
Wilson has been without 35-goal striker Ched Evans since he was jailed for rape last month, while James Beattie is in the middle of a four-game ban.
Chris Porter ploughed a lone furrow up front for the Blades in the first leg, but Cresswell is hoping to overcome a shoulder injury that has required injections in recent weeks.
Wilson has been a consummate professional in dealing with both the loss of Evans and the crushing disappointment of missing out on automatic promotion, and despite a job well done by his players on Friday night is wary of complacency.
"It's finely balanced and we can't take anything for granted," Wilson said.
"We know we have to have the same determination at Bramall Lane. We'll be very careful, we don't want to get carried away. We still have a lot of work to do.
"We see too many times when people make assumptions after the first leg result and form a conclusion - you don't know how it's going to pan out.
"Stevenage went for it on Friday night and we stopped them. The three games between us have been very tight."