i analyzed the game and saw that the level of inaccuracy and mistakes were lower compared to my opponent. But, i could not win and offered a draw. It was accepted. Was there any chance of me winning in the end?
@gablusky being up a rook can seem a little nebulous if you're looking for a concrete way to convert your advantage. In this case, your opponent has one piece (the queen) to defend most of his pawns. You have two pieces (a queen and a rook) to attack any of his pieces. There are two ways to go about using your advantage here:
1. Force a queen trade - if you traded queens your advantage goes from 2 pieces to 1, to 1 piece to 0. With your rook unopposed you can take as many of black's queenside pawns before his king can spring into action. In the final position black seems to be able to resist a queen trade, so this might not be the best option to explore first in the position.
2. Attack your opponent's pawns one by one - since you have two pieces to attack and he only has one to defend, you can attack any pawn in the middle or left side of the board with both pieces at once. For example, you could start with Qd4 or Rd4, attacking either the d6- or f4- pawn with two pieces. Black has no way of supporting his pawns when you focus them one at a time.
One last note, because it seems like it could apply here. When your opponent has a lone queen left and your king is slightly exposed to checks, sometimes it can be good to visualize a position in which you're checkmated by the lone queen. In the final position, the only way you can be checkmated is if your king is on h1 and the black queen is on f1. If you know that's the only position you have to avoid as you go about picking off pawns (and eventually promoting one of your own), it can set your mind at ease and mitigate some of the anxiety that comes with being checked repeatedly.