Cos professional football is not Football Manager or Fifa. He doesn't do the deals for players. If he was needed he can be contacted easy enough. Koeman stated many times he wanted a striker and a left sided central defender and maybe cover for Baines. He said he had made the board aware of what he wanted. That suggests to me that he's not the one bringing the players in.
It would seem that he highlights areas that they need and someone else identifies the players. Perhaps Koeman has final approval on the player, and in some cases even highlights the player himself.
If Llorente had the choice of Spurs (London) or Everton do you think Koeman being at FF would have made a difference? He had the choice of Chelsea as well by all accounts.
There is certainly something wrong under the surface at Everton in how the Summer transpired. My guess would be a disconnect between Koeman and the Club/Walsh.
That doesn't excuse the fact that the side doesn't appear to be set up correctly, but let's not forget we played Man Utd away, Man City away, Chelsea away, and Spurs at home, while trying to bed in new players, and playing twice a week with the Europa games. In all fairness Moshiri's statement that the Burnley game is the first unexpected loss, probably isn't that far from the truth and if Sig puts that chance away early, no doubt that'd be a very different game as well.
Last season we had a run where we only won 1 game in 13 or something when he was giving the senior players a chance, before then opting for a more youthful set up and a great run of results. He's got out of this situation before and I fully expect Koeman to do it again. Then hopefully come January the obvious gaps in the squad will be addressed.