You should be bothered in a world where sports fans care more about winning championships than they do about getting a single result against a rival or advancing past the opening round of a tournament.
It would be one thing if you supported Burnley. Hell, it would be different if you, like me, were supporting City in the early 1990s. But Spurs has finished in the top 4 the past few years, largely because of Poch. If your team has the capability to challenge for trophies, your ambition should be to win trophies—not simply to line Daniel Levy’s pockets. And if Spurs fans don’t give Levy stick for this shit, you’ll get what you deserve—Poch will leave, along with your star players, and you can go back to hoping you make it to Europa every few seasons.