After such a bruising night Clarke will, in his private moments, be questioning his side and set up before facing Switzerland in Cologne.
Should Billy Gilmour come in to help keep the ball better? Does Gunn need replaced after a shaky performance in goal? How can Scotland be more of a threat?
Ally McCoist, the last man to score in a Scotland win at the Euros against Switzerland in 1996, says they need to look for solutions quickly.
“Scotland have to change their mentality ahead of their next two games,” the former striker told ITV.
“Scotland have to get balls into the box, get players forward. There has to be a completely different approach.
“It should be slightly easier now as I don’t believe the other two teams will be at the same standard. They are good teams, but not as good as Germany.”
Thompson believes Clarke needs to think about changing shape to sharpen up in attack.
“We didn’t see the width, Robertson and [Kieran] Tierney combining is one of our biggest weapons,” he said on Sportsound.
“I’d like to see us play with a winger. James Forrest or Lewis Morgan. Because we did not offer any threat. We’ve got to offer more and tactically be different.
“I would think about a change in formation.”