Clarke said the nature of Hungary’s winning goal was a result of Scotland’s desperation to win the game at the other end.
Kevin Csoboth finished off a counter-attack in the final seconds after Scotland piled players forward, and Clarke says they did not have the luck they needed.
“You’re always to get caught when you open up like that,” Clarke said.
“We did create some chances. A consequence of being under pressure to win is maybe you snatch a bit at those chances.
“Sometimes you need the footballing gods to be on your side; they weren’t on our side tonight. It’s a cruel game. We all suffer the same.”
The Scotland head coach says his side must now turn their attentions to qualifying for their next major tournament.
His squad are next in action in the autumn, when they face Portugal, Croatia and Poland in the top tier of the Nations League.
“You have to lick your wounds, refresh yourself and go again because it can’t be another 26 years before we go to another major tournament overseas.
“That’s got to be the next ambition.”