Against a better player

The first mistake I actually see is on move 23 when you allowed black to transform a doubled pawn into a passed pawn.  Doubled pawns are weaker than passed pawns; or, in this case, the passed pawn is stronger than the doubled pawns.  Granted that at this point I haven't taken a look at the rest of the game, but I suspect that as the game goes on, that pawn will be the difference.

Second thing I see is that now that you have a passed pawn to deal with, you made the mistake of trading down material.  Your pieces have to be on the board so that your opponent doesn't make use of the passer.

And I was right as to how the passed pawn came to be the decider.  Do not allow your opponent to strenghen the pawn structure after you have weakened it.