Clarke’s side came from behind at Hampden to beat Kazakhstan 3-1 with a double from Aston Villa’s John McGinn either side of captain Steven Naismith’s tenth goal for his country.
Scotland now go into Path C of the Euro 2020 play-offs and will face one of four possible opponents – Bulgaria, Hungary, Israel or Romania – in the play-off semi-final at Hampden on 26 March.
Uefa will hold a draw at 11am on Friday to determine which of the sides Scotland will face.
There will be a further drawing of lots to decide the venue of the play-off final.
If Clarke’s squad make it to the final, they will face either Norway or Serbia in another one-off fixture on 31 March.
The Scotland manager said: “With this group of players, I can be very optimistic about the play-offs.
“I know what they are thinking. They are 100 per cent committed to their country and are desperate to get to a major finals at Euro 2020. So we can be very optimistic.”
Clarke is looking forward to discovering Scotland’s semi-final opponents but is not concerned about who they are paired with.
“I’ve got no preferences,” he added. “Always with a draw, you take what you get. But it will be nice to have a little bit of clarity so we can actually start planning for the March games.
“We’ll be at home [in the semi] and I think we’ve shown tonight we can be a good team here at Hampden.
“The place will be full that night, I’m sure. We’ll get a good atmosphere and if we get the team on the front foot, we can be okay.
“I thought the performance tonight was good – good in the first half and really good in the second half against a dangerous opponent.
“We knew if we made mistakes in possession, Kazakhstan could hurt us on the counter attack which they did when they took the lead.
“But it was a great reaction from the players, in the second half particularly.
“We played a lot of good stuff, looked a threat going forward and created a lot of chances. Nine shots on target is good,” added Clarke.
“It’s another win – three wins in a row. I don’t know about anyone else, but the boys in the dressing room are feeling good about themselves.”