Can a knight stop a rook pawn?

my opponent gave me a draw ... i think i should have lost.

Game 872305

It's drawn. For example
1. ... Kf5 2. Kb5 Nb8 3. Kb6 Ke6 4. Kb7 Nd7 etc.

I needed to play 34. a4 to try to keep the pawns connected for any hope of winning - but I didn't cotton on in time.

Draw indeed. White doesn't even need to bring the king closer.
Example: Nb4+ Kb5 Nd5 and
- a6 Nc7+
- Kc6 Nb4+
- Kc5 Nc7 etc...