What would Klopp say if this non-story actually came to something. "We didn't win our last game because the opposition scored a goal during a phase of play which saw them in an offside position". Ok, end of discussion.
Yes, that was probably the message he wanted to convey through sarcasm. Hence the need to "explain", "clarify" etc, as other managers and players had to do, it's not a big deal. Is he better than Sagna, or Wenger for example? Intentionally or not, he implied that Liverpool does not have the same treatment by the referees as other teams. I don't mind it, that's what managers do, but both you and I know how annoyingly inconsistent the FA can be (and perhaps will be in case of Klopp's bitter comment).
I'm sure if Klopp came out with something anywhere near what mourinho said he would be sanctioned too.
Fact is he used a general term with the word "teams" think that's the difference. Sagna referred to the ref as did mourinho.
Who did Klopp refer to then?
If Sagna's "10 against 12... but still fighting and winning as a team" Instagram remark was considered to be a reference to the referee, and had to be explained to the FA, so should be Klopp's "...most of the teams play against us without offside rule".
As for your other point, by using plural he made it sound worse actually - as if it was a frequent occurrence in Liverpool's games, suggesting they were more than once exposed to unequal and unfair treatment by the refs.