Lewis Ferguson – in his first Scotland game for almost a year following his return from knee surgery – was keen to shine a light on the “dirty side” of the performance.
“We knew we were going to have to weather the storm,” the Bologna captain said.
“We could have been calmer on the ball, but you need to show that side of the game if you’re going to get results away from home – the dirty side, the running, tackling, blocking, heading.”
Scotland could have been further in front at the break in a fine first-half display.
Billy Gilmour shanked wide, Che Adams shot straight at Konstantinos Tzolakis with the goal at his mercy, and the Torino striker then fired another effort across the face of goal as Scotland repeatedly hurt Greece in transitional moments.
Clarke praised how his players troubled their hosts, but is taking nothing for granted before Sunday’s return leg at Hampden – live on the BBC – as Scotland try to preserve their top-tier status in Nations League.
“First half we were really good, we could’ve been two in front,” he added. “If I’m being greedy I could say three. This game is not dead yet. No way.”
