Scotland will end a 23-year absence from the big stage at this summer's Euro 2020 finals but the focus is on the World Cup as Clarke's men begin their qualifying campaign against Austria on Thursday.
Clarke said: "The squad is focused completely on the World Cup games because they are the most important ones.
"We have said almost since we qualified for the Euros that we don't want to be one-tournament wonders. We want to have a continued period of success.
"That starts tomorrow night against Austria at Hampden."
Clarke lost Rangers midfielder Ryan Jack to an ongoing calf problem on Monday but has the likes of John Fleck and Kenny McLean as alternatives, while Scott McTominay could move forward into his natural midfield position.
"We lost Ryan Jack but we sort of pre-empted that so we are in good shape," Clarke said.
"It is a blow because he has done well for us and he plays a certain position in midfield that without him we don't really have. We will miss him but we have got a really good squad now so time for someone else to step forward.
"The little time we have had on the training pitch has been really good work, high quality so hopefully we can take that on to the pitch. In my head, I know the team."
Austria have also qualified for the European Championship, for the second time running, but like Scotland have not reached the World Cup finals since 1998 when they finished above Craig Brown's side in their section.
The visitors faced being without 19 German-based players but more lenient quarantine measures came into place just in time for them to include the likes of Bayern Munich defender David Alaba.
"They are a good team," Clarke said. "I think their strength is probably in the team rather than individuals. Like any Austrian team, physically strong but good technically, dangerous in certain areas of the pitch.
"We will set up to try and nullify that but we want to be on the front foot as well, we want to make sure we cause them a lot of problems, which I think we can. Sometimes we play ourselves down a bit in this country.
"I think I have a good squad of players and we can get better and better, to do that we have to beat teams of the standing of Austria."
Scotland have only scored three goals in their past six matches and Southampton striker Che Adams and Hibernian forward Kevin Nisbet have been called up for the first time in a bid to address that record.
But Clarke said: "You always want to have a goal threat but I think we have shown also that if you keep games tight at international level, one goal can sometimes be enough to win a game.
"In the two games we lost, one was enough to lose the game. So at international level, you always have to be solid."