Kinda hard to answer... not sure what you mean.
I'd say in general it's important to be accurate when there are tactical elements (like an open position with undefended pieces, a loose king, etc). It's also important to be accurate when there aren't many pieces left (if you lose a pawn in the opening that's less than 1/10th of your force, but if you lose a pawn in the endgame that's a lot more).
In your game I imagine you were struggling with piece activity more than accuracy. On a crowded board it can be hard to find an active place for your rooks, while knights and bishops tend to fare better. Also since minor pieces can bully major pieces, your opponent was probably able to chase you around without much trouble. Depending on the position you may have had the worse position even though by the basic count you were ahead 1 point.
I recently played a game wherein I had a queen and two rooks versus two bishops, a queen, and a knight. I was struggling to play accurately, so that is why I thought of the question.. or does it just depend on the game?