Last season's Irn-Bru First Division runners-up replaced stricken Rangers in the top-flight, after the Glasgow giants were voted into the Third Division when the club was consigned to liquidation.
Dundee began their SPL campaign with a respectable goalless draw at Kilmarnock on Saturday but Smith - who hopes new signing Davide Grassi will be granted international clearance on Monday - is keen to strengthen further for the challenges ahead.
He said: "If you look at my bench today, I had four under-21s and one on the pitch.
"These boys haven't really played in the First Division so to throw them into the SPL is a massive ask.
"We think they are capable but we are looking for guys who can play at that level.
"We are always looking and hopefully in the next couple of days we will get a couple more in but that's not guaranteed."
Both sides were forced to settle for a share of the points in the curtain-raiser at Rugby Park and Smith was keen to pay tribute to a travelling support of around 3,000 for playing their part.
He said: "Kilmarnock is a difficult place to come to so we are happy to go away with a point.
"We would have taken a point before the game so we are happy.
"The overall performance was credit to the team, the way they worked and how hard they worked.
"The crowd also spurred them on and were fantastic. To bring a crowd like that is incredible and it's brilliant to see them get a boost from being in the SPL.
"The difference between the First Division and the SPL is consistency. We need that level of performance every week.
"I hope we can do it. That's why we've brought these players here, because we believe we can."
The SPL opted for Dundee, rather than relegated Dunfermline, to replace Rangers.
Asked what he would say to those who claim the Dark Blues do not deserve their place in the top-flight, Smith said: "You just have to look at the support we brought down today. That's good enough for me."
Killie were without Paul Heffernan, who has a broken collarbone, for the visit of Dundee, while last season's star man Dean Shiels sealed a move to Rangers this week.
Assistant boss Jimmy Nicholl said: "It was frustrating because we would have liked to score goals.
"We don't have Heffernan and Dean Shiels - and that's 30-odd goals and assists for the team.
"We were hoping we would get a bit of joy.
"We knew what our problems were going to be and we just couldn't score when we were on top.
"It was disappointing to be honest with you."
