How to tell that this is a draw In an endgame I played as Black, after the rooks were exchanged, the below position was reached. A funky stalemate quickly ensued.

[FEN "8/5ppk/5p1p/8/3K1P2/6P1/7P/8 b - - 0 1"]
[startflipped ""]

1... Kg6 2. Ke4 Kh5 3. h3 g5 4. f5 g4 5. h4


It was a simple endgame to me. as Black, I had an extra pawn and was closer to my pawns then White. I would just exchange pawns and promote my extra. I though that I would win until I stumbled into an unexpected stalemate. Not a big deal, mistakes happen.

But when I put the position into Lichess, surprise, surprise, it was actually a draw! It turns out that White will be able to lock in Black, using Black's doubled pawns against them, and forever keep Black king imprisoned for eternity, thereby drawing the game.

What could I do, without computer analysis, to determine that this and similar endgame positions are a draw? What endgame principles are there/exist that would help?
I had an extra pawn and was closer to my pawns then White


It seems you simply overestimated these two factors. 

An extra pawn alone is not a decisive advantage, it matters a lot where it is located. If the f7 pawn was on a7, you'd win. 

The kings are actually positioned to your disadvantage, White's is nicely centralized and yours is stuck in the corner. If the White king was on g2 and yours on e4, you'd win.

But most of all, chess endgames are concrete. If you shift the whole position one file to the left, the engine does indeed see black winning! 

What makes your position a draw is the unfortunate pawn formation: Your own doubled pawns trap your own king in the corner, while White's are flexible enough to shut the position from the front. And as said, his king is well positioned, it can either block the escape of yours via d8 or assist his own pawns in preventing the frontal breakthrough.