You can extrapolate the discussion more broadly pretty easily to be generally a discussion of when you think a manager deserves the sack. Does Mourinho deserve the sack? You've improved a bit, but the football is pretty dull and you don't look any closer to winning anything despite making a final and then being unable to break down the bus parked ahead of you.
I don't think he deserves the sack this season. You've made improvement in the league, so results have improved even when performances have not. And you're a hard to beat side. But if next season goes similarly to this season, where you maybe make a cup final but can't break down the side ahead of you and make top 4 comfortably but don't win it. Maybe the performances have been much improved though or something to give some fans reason to believe some sort of improvement has happened... but it's again, another disappointing season. Do you sack him? Or do you keep him?
But I guess it can be hard to compare the two, because the circumstances are different and like I said... this is all circumstantial. With United fans, I know there's already a group that thinks Mourinho should be sacked ASAP - I think right now Klopp's got 99% of fans onboard despite not having ultimate success in the CL final. Also Klopp's done a lot more building with the squad and the side - he's done a lot to not just bring in players to improve us (and he's done quite well in the transfer market) and improve the performances of those already here pretty substantially. I don't think many United players have had the same kind of role transitions and flourishment we've seen from either Firmino or Lallana, for example. Regardless of the fact that bringing in Matic was a great move (and probably his best move at United).
I wouldn't sack a manager that's making any sort of upward trend though, whether in results, performances on the pitch, ideally both, or building a side that's got quality and depth and demonstrates it. I'd only sack a manager after a pattern of regression that demonstrates the rot cannot be stopped by the man in charge.