EDINBURGH, Scotland — When the second goal went in, Ian Cathro felt a shift. Cathro, the Heart of Midlothian coach, had not given up on the game: His team was down by only 2-1 to visiting Dunfermline in their Scottish League Cup match, with much of the second half to play. There was still more than enough time to draw level, perhaps even go on to win.

But the 31-year-old Cathro could sense enough of a change in the “ambience” to know that saving face would not save his skin. He had been in his job for only eight months. Right from the start, the pressure had been such that at points, he joked, he thought his “first name was Under Fire: Under Fire Ian.”

He had tried to block it out, to get on with his work, but he was not blind to it. He knew it well enough to realize that second goal, he said, meant “the fires had been lit.”

He was right. Two days later, Hearts’ director of football, Craig Levein, called Cathro into his office. The two had known each other for more than a decade. Levein had, for some time, been a sort of patron and mentor to Cathro. Now, though, the men had to have a “short, unpleasant conversation.” A few hours later, Hearts issued the stock statement, full of platitudes, documenting the dismissal as a “difficult decision, made reluctantly.”