The Scots play host to Serbia at Hampden on Saturday, before facing Macedonia three days later at the same venue.
Naismith is confident the national team is as ready to deliver the goods now as they have been since Levein replaced George Burley at the helm in December 2009.
He said: "Nobody can deny that there has been a lot of progress made from where the national squad was before he took over. We've all now had experience in qualifiers.
"It's not as though we are a new squad coming together, we've been together for a while now, which goes a long way.
"Now we need to turn it into performances at the qualifying stage, not doing it in friendlies and things like that.
"We now need to show that we are capable and that what the manager has been working towards has paid off."
Scotland face a tough group, which also includes Belgium, Wales and Croatia.
But the Everton midfielder added: "We are confident. The group we've got is going to be tough but we think we can get results.
"There is enough experience along with youth in the squad to compete against anybody."
The Tartan Army will no doubt be looking for a maximum six points from the opening two matches.
Naismith is well aware of the demands for success but believes the national team are in decent form following last month's friendly win over Australia.
He said: "In the home games there is always pressure. Since I've been in the squad we have shown up well in the home games, we've competed and we've probably been the better team against most.
"It's just about turning them into wins.
"Looking at the fixtures, I don't think you can get better than the two home games, to have the fans behind you and hopefully get a good start."