After being appointed as Leicester manager until the end of the season, Smith began his tenure with a 3-1 defeat away to Manchester City last weekend.
Although Smith would have been disappointed to concede three goals inside 25 minutes, he would have been encouraged by his side's second-half performance, which included a consolation goal from Kelechi Iheanacho.
However, the former Norwich City boss will be aware that results rather than performances are needed if the Foxes are to stay up, with three points separating them from safety.
Having picked up just one point from their last nine league games, Leicester will be looking to end their winless run against Wolves on Saturday.
The Foxes will go into the contest without the services of Barnes, who will miss a second straight game due to a hamstring problem.
Speaking in his pre-match press conference, Smith revealed that he did not want to risk the Englishman for Saturday's encounter.
Smith told reporters: "Harvey Barnes is ready to go on the grass, he's been on the grass, but he's not actually trained with us yet.
"I think it would be a risk to put him in on Saturday because we could lose him then for the six games. I've got to balance that risk. I know he will start training on Sunday and then be ready for Tuesday. It wasn't an easy decision, he's our top goalscorer.
"He wouldn't have been able to start this weekend, it would have been too quick for him. But he would have got minutes off the bench. The risk for him to re-injure was too big for me, so Tuesday's a more realistic goal for him."
Jonny Evans is unavailable due to a viral infection, while Ricardo Pereira is still two weeks away from returning to action due to a hamstring injury.
Smith revealed that Jannik Vestegaard will miss the rest of the rest of the season after picking a calf injury in Monday's Under-21s game.
Ryan Bertrand, who has been out of action all season, played 65 minutes in the Under-21s match against Manchester United to put him on the verge of a return to the first-team squad.
Youri Tielemans is expected to start once again after playing an hour against Man City on his return to action following a spell on the sidelines.