The Scots reached their first major tournament for 22 years when they defeated Serbia in a nerve-jangling penalty shoot-out in Thursday's play-offs.
Footage of Clarke's players drinking, singing, dancing and doing a conga emerged from Belgrade dressing room as they celebrated a famous success.
But Clarke insisted they had now set aside that achievement and were fully focused on gaining more success in the Nations League.
Scotland will guarantee top spot in Group B2 and promotion to the top tier plus a potential World Cup play-off place if they win one of their remaining two matches against Slovakia and Israel.
And Clarke believes the effects of Thursday's celebrations will have no bearing on his selection for Sunday's clash in Trnava.
Lyndon Dykes will drop out through suspension, while Andy Robertson is a doubt with a tight hamstring and other players will be assessed.
When asked if he would make more changes than normal, Clarke said: "The short answer is yes. The long answer probably takes in the fact the celebrations wouldn't have anything to do with it. It was a good celebration but it wasn't crazy, it wasn't silly and over the top.
"I trust all the players, that's why I select them. The ones I brought into the camp last month, I trusted them and they deserved to be on the pitch.
"I watched the training session this morning and I said to one of my coaching staff, they are already playing for their place at Euro 2020. I could see it in training.
"And that's what it's all about. That qualification is in the cupboard, it's something waiting on us next summer, and all the lads can put themselves in the squad by their performances in the camp or out the camp."