I think people often get the wrong end of the stick about fixtures. It's not that players nowadays are lazy or for 100k a week they should be able to play three times a week etc, it's about getting players close to their peak for the game.
99% of them would play four games a week if they could but they would fade badly after 70 minutes. We've seen it ourselves; I remember under Jones there was a season where we'd always concede after 85 minutes, and another season under Mackay where we always felt we'd score after 85. That wasn't luck or tactical, it was simply that the team as a whole was better conditioned than the opposition. Most goals come from individual errors, and tiredness increases the chance of making an error as everyone who's played at any level will know.
I don't know what Klopp's problem was exactly, but I'd imagine it was to do with other rival clubs getting more rest days in between matches.