It’s not the criticism itself that is anti-Semitic. There’s plenty of criticism of Israeli actions and politics that don’t come across that way.
But you can tell who’s anti-Semitic by they way are attracted like moths to a light bulb to any story that has some connection (regardless of how distant that connection is) to Jews or Israel to get on a soapbox about how bad Israel is. And when confronted with accusations of their anti-Semitism, they rarely deny it. Instead, like you, they try to turn it around on the accuser.
It’s similar to the way you can tell who’s simply angry at his wife over a recent spat, and who’s a misogynist.