Think of how deep that statement goes for Jon, though,
"I can't save anyone."
How constantly he must be reminded that there is no place to rescue anyone to. There is nowhere that Sam or Maeve or Sabina can go where they will not be tormented. That alone is enough to make him lose hope, but it's more than that.
From the very beginning of the season, Jon has been utterly unwilling to even try and help anyone. I think part of it is also trying to cope with how much guilt and responsibility he already feels, and his inability to comprehend having even more of either. Because if he saves someone, anyone, then he has to cope with the millions of people trapped behind them, and he has to be responsible for deciding which one to save. It becomes a choice, not a circumstance that he has no control over. That can't becomes a didn't.
"I didn't save everyone. I chose not to."
And maybe, he will always have in the back of his mind, maybe he could have. But he didn't.
I don't think Jon left the cottage really believing they were going to save anything. Least of all not the whole world.