Two things I think might help:
1) FAITH/MENTAL SUGGESTION: The really good ones have the mind-set that they WANT the ball it to THEM, rather than to anybody else...they simply BELIEVE they have the best chance of making the play and helping the team. And, they have that attitude EVEN IF they've just "booted" one. Without trying to offend anyone, it can be somewhat like religion...faith in something you cannot yet prove. Maybe a better way to describe it is a form of self-hypnosis: You put yourself in a "receptive" or "suggestive" state-of-mind and, then, impress the thought you want upon that mind.
2) MENTAL PREPAREDNESS: The really good ones have ALREADY made the play...IN THEIR MINDS. They KNOW the situation (i.e., who the runners are, whether they're fast or slow, whether they're getting good leads or whether the pitcher is holding them tight, who the batter is and how the picher is throwing to him (i.e., does he "pull," is he a line-drive hitter, what's his foot speed, is the pitcher working him outside or in, is he throwing something off-speed, what's the count). All these variables and likely possibilities are assessed BEFORE the pitch is ever delivered and WELL BEFORE the play must be made (i.e., on a hard ground ball hit to my left, if I field it cleanly, I do this; a soft grounder to my right, if I can't field it cleanly, I do that; for a line drive, I do something else). When the ball is put in finally put in play, the one's who've done this exercise already KNOW what to do...they've removed "indecision" from the equation and, often, ANY decision. All that's left for them is to EXECUTE the plan/decision they've already made. This approach requires the mental discipline to STAY IN THE GAME and to go through each possible scenario in a very fluid/changing environment. But, it should yield BIG dividends by giving you the confidence of ALREADY KNOWING what you're going to do, having already played out the scenario (successfully) in your mind. When the play ultimately develops JUST LIKE ONE OF THE SCENARIOS YOU ENVISIONED, its very rewarding and should inspire confidence and trust in yourself.
It should be noted that these two things are complimentary. Hope this helps...GOOD LUCK!