caro-kann game

You blundered the endgame.

Your 4th move is a mistake, and White's opening line of play is horrible!

1.e4 c6 2.Nf3 (This move is ok if followed up correctly) d5 3.exd5? (This is a serious error - 3.Nc3 is better here - explanation why is below) 3...cxd5 4.d4 f6?

Black's 4th move is a serious error.  The first thing Black should do is say THANK YOU to White and play 4...Bg4!!  Black will be given the opportunity to trade off his worst piece, and has an easy game.

Compare this to the theory of the Exchange Variation.  1.e4 c6 2.d4 d5 3.exd5 cxd5.  At this point, White has two decent options.  4.Bd3 and 4.c4, the former being the true "Exchange Variation", the latter being the Panov-Botvinnik Attack.

After 4.Bd3, the onus is on Black to come up with Good moves.  Think about the position, you basically have an Exchange QGD with colors reversed.  Many times in the exchange QGD, Black puts off ...Nf6 so as not to give white Bg5, and tries to make White develop the Bishop to f4 before moving the Knight out.  The same holds true here.  Black would really like to trade Light-Squared Bishops or trade his LSB for a Knight.  With an early Nf3, like 4.Nf3? (A mistake, directly transposing to the game in the OP), Black gets 4...Bg4 as a gift!  with 4.Bd3, Black has to find moves.  He can't go to f5 with the Bishop due to White's on d3 just taking it, and even if he could and it wasn't taken, going to g4 would lose a tempo after White plays Nf3 at that point, and he doesn't want to play ...e6, blocking the Bishop in.  So Black typically plays 4...Nc6 here, answering 5.c3 with 5...Qc7.  Now White still shouldn't play 6.Nf3?, and instead go 6.Ne2, threatening 7.Bf4.  Black now plays 6...Bg4, and after 7.f3, goes back with 7...Bd7 (avoiding checks with Bb5), and answers 8.Bf4 with 8...e5!! intending ...Bd6 and ...O-O.  If White takes with the d-pawn, Black takes with the Knight and White can't take advantage of the pin fast enough for it to be relevant.  Black gets out of it with ...Bd6 and ...O-O and has already achieved equality.

Black's game is even better than that if White allows him to play ...Bg4, pinning the Knight to the Queen, and often trading Bishop for Knight, but you wait until you are forced to do so, as in White plays h3, putting the Question on the Bishop, then you take.  Don't give White a free tempo, make him spend time on h3.

Wow, forget the endgame.  This entire game was Blundelicious!  White's 3rd move is bad, Black's 4th move is horrible, Black's 5th move is a Blunder, Shoot, White's 56th move is a blunder!  The simple 56.Kf5 and now what?  If 56...Kh7, then 57.Ke6 intending 58.Ke7 and 59.f7 winning.  If 56...Kg8, then two different lines both win.  The basis 57.Ke6 Kf8 58.h7 (58.f7?? Stalemate) Ke8 59.h8=Q# or the more flashy 57.h7+ Kxh7 58.f7 Kg7 59.Ke7 wins easily.  Takes longer because now you have to make KQ vs K, but Black can prolong the same thing after 57.Ke6 Kh7 58.f7 Kxh6 59.f8=Q+ and again you have KQ vs K.