Can anyone analyse why I lost?

Opening principals were not followed, but at least in this game that didn't matter too much because the position became closed. Still, for the sake of improvement it will be useful to try to follow the opening principals.
---
The main reason you lost is because your rook became trapped. Usually the player with more pieces is winning. Objectively speaking, after you lost the rook your position was losing.
On move 34 you don't want your rook stuck defending the pawn, so it was good to instead play 34.f3.
You also don't want your rook to be blocked by pawns on its file (i.e. the e file is closed). All pieces like open lines. Your rooks want to either be on h1 (the only open file) or for example b1 (and then you can play b4 and open the b file).
---
The move you played instead, 34.a4, was also bad on its own merits. The pawn at the bottom of a pawn chain (the undefended pawn in a diagonal of pawns) is the weakest pawn. Your move 34 moved the weak pawn from a2 to b3. The a2 pawn was weak, but difficult for black to attack, but b3 is on a half-open file. After your 34rd move, the b3 pawn is also what's called a backward pawn (which is a weakness).
This isn't why you lost, but it's a useful way of thinking about pawns.