I assume the mistake was the end game?


One very important rule that my former coach told me is to NEVER EVER Trade down to a pure king and pawn endgame unless you are damned sure it is in your best interests to do so (either you can win it cold or steal a draw based on your knowledge of K + multiple P endgames) .
With that being said, Ra5 was not necessary as you pointed out. ... you were in no trouble and actually white's rook looks a little trapped.
Perhaps ideas like 37...Bc4 takes the heat off of your d5 pawn. Then maybe after 38. Rb4 Ra5 and your rook is way more useful looking than his.
In addition to what shivsky said I would also like to criticise a4. The move was not necessary and weakened the b4 square as well as putting the pawn on the wrong colored square (in endgames its usually a good idea to put pawns on oposite colored squares compared to the bishops). Instead I would suggest activating your king first.
Also senses should start tingling when you have to make moves like Ra7 to defend your pawns, indeed its difficult to suggest an easy alternative there though.
Still I think it would be wrong to just criticise your game, for the most part it looks like a very good game for someone of your rating. I think you played very energetically and inspired. I think you wrongly criticised 15. ... Bg4! The initiative is very important and not a moment should be lost in the attack! After 16.Qxd5? I think you would already be winning after 16. ... Rad8! Regardless of where the queen retreats you would win with the moves 17. ... Bxf3 and 18. ... Nd4 -+ for example 15. ... Bg4! 16. Qxd5? Rad8 17.Qc4 Bxf3 18.gf Nd4 19.Rd2 Nxf3+ and white can resign.

Ra8 was a stinkbomb. You called it as too passive.
What does a stinkbomb mean in this context? :)
But thx for all the advises so far, guys :)

some synonyms:
obviously bad
lame
worthless
counterproductive
oh well...may you please suggest some alternative?

Don't slide your rook into a corner in an endgame. Passive rook moves generally signal a slow and painful demise.
Re8 would have cut off the enemy king from the Q-side
Rc1+ looks good but doesn't seem to go anywhere after Ke2

Wow. All these comments and so far nobody has pointed out that the endgame after the trade of queens already favored White.
Yes, you botched the Rook ending completely. But you were already stuck defending the poorer position because of the isolated and backward pawns, the less active pieces, and a lack of targets for Black.
The position at move 24 is already in favor of White. Your endgame plan was far too passive, but your judgement that the endgame may have been equal was also at fault.
Others have made some excellent comments, but you also need to take a look at the endgame before you get there! If the endgame is inferior for you, look for ways to keep the middlegame going. You may have found Onelastbreath's idea if you had been looking for it.
Fezzik, why do you think white has the advantage!? Granted, white has better peices but surely Black being up a whole pawn is sufficient compensation?
I would rather play black any day of the week.
Black was just fine after the Queen trade and Bb3 (good idea) If you hadn't played the horrible a4 and Ra8, and focused on playing with an active rook and king, you would have had the advantage. The isolated pawn is hardly a weakness, as its easily defended without detracting from other plans, and white has to continually worry about it.
After 26, Bd3:
white can play Re8, making it harder for whites king to get into the center, work on centralizing his king (if you imagine this position, except with the king on D6, black is totally winning. King on d6 and rook on e8 -- it would be hard to lose). I dont see how people can say that black has a bad pawn structure -- hes up a pawn, and a passed one at that. If you took this same position and took the pieces off, white doesnt stand a chance.
Blacks bishop is better than whites, and blacks rook is easily made more active than whites (he has to always keep an eye on the central pawn.
White has no real way to target the pawn on b7, and if the pawn moves to b6... even less ways.
One idea for black is that he has good chances of trading at c4 and winding up with a 3v2 or 2v1 majority on the queenside.
Basically, after the position around 26. Bd3, with decent play black would have no problem activating his king, the kingside pawns might move up a bit, trade off the rooks and bishop, which of course results in the white king being forced to the queenside, with the queenside being liquidated, and the black king running back over and eating the kingside pawns -- a couple of moves ahead of the white king, no less, and at this point, any class player could win against Kasparov with black.
***
BTW, I plugged this position into Fritz 12, which scored it at around -/+ -1.11 @ depth 18, and around - 1.00 after BxQ, and -1.3 before ... Qc2

Obviously, many endgames mistakes :
1- rooks endgames are the only endgames in which activity counts as much as in middlegame : moves 27...Ra8 and 28 ...Ra7 (definitely trapping it) were very bad.
2 - whith same-coloured bishops, try to block the opponent's pawns on the color of the bishop (see move 26 ...a4 ? , worse than useless)
3 - a doubled isolated isolated pawn is worth only one in K+pawns endgames ; because of zugzwang it won't be able to defend well. With some pieces on the board it is worth two in defense against 2 linked pawns. And as K+p endgames are 90% wins for the side with material superiority, it counts.
And a last advice against this opening : (this is my personal experience, take it as you want)