The Alexander Technique was developed when a 19th Century actor was having trouble with his performances. His voice would not work physically because he knew that soon he was going on stage and had to speak. The first time I learned about the Alexander Technique, one fix was described. Instead of saying to himself that he had to go on stage and speak, then starting a process that left him with vocal problems, instead he told himself, 'I don't have to go on stage, I don't have to speak' and that stopped the escalation of his vocal problems.
If you tell yourself that you have to hold serve or that you need to win the next point that may start a physical process that affects your serve. Tell yourself 'I don't need to hold serve', 'I don't have to win the next point'... for whatever issue came to your mind. This can also be helpful in doubles when your partner starts saying what 'we gotta do', "We just have to hold serve and we win." I've replied that 'No we don't need to hold serve. " etc. It takes the tension down quite a bit. Often I get a laugh out of my partner when what I said is nonsense, as it often is.
The next time you have a 'must do' thought and feel tension, simply tell yourself that you 'don't have to do' whatever it is.