As players get better, it becomes more and more difficult to figure out why one person wins the match and the other does not.
The best players seem to win more of the points at the crucial times. It would be natural to assume they lift their game and rise to the occasion, therefore resulting in success most of the time. In reality, the best players play the points exactly as they would play a random point at different stages of the match. They are less influenced by the score and know that if they play their regular point, it is good enough to win the majority of the time.
A player who is not quite at that level tends to try to play better than normal, or they play more cautiously, hoping not to make the mistake that will cost them the match. In addition, the best players are great at having a "convenient memory". They remember all of the good things that have happened and immediately erase all of the negative thoughts from a bad point or shot that has just occurred. This is what allows them to execute at such a high level under so much pressure.
Try using the old adage: "play every point the best that you can" regardless of the score. This will likely give you the greatest chance for success on the "big points".