MANCHESTER, England — Jürgen Klopp was walking along the edge of the Old Trafford field, on his way from the locker room to speak to the assembled news media, when Liverpool’s fans spotted him.

They had been corralled inside the stadium for 20 minutes or so after the final whistle, until the Manchester police had determined it was safe for them to be accompanied out. They had entertained themselves by singing, for a while, but had gradually fallen quiet, as if trying to work out their emotional reaction to the 0-0 draw they had just seen.

And then Klopp appeared. As they lingered in the aisles, ringed by stewards, they turned to salute him. “Liverpool, top of the league,” they sang. Klopp had spent most of the afternoon with a deep-set scowl on his face, barking instructions at his players, bristling and bubbling with dissatisfaction.

As he got closer, though, as he worked out what they were singing, he put one hand on his heart — on the Liverpool crest on his top — and, with the other, offered a little wave. He beamed that broad, warm smile, the one that makes him look a little like a happy shark. It lingered even as he turned away, before he got serious again.