|When employees believe their manager does not listen, they typically try to find someone who will, and they often look up the corporate ladder to find that set of ears.|
It is possible that everything they wrote is wrong, but it is also possible that there is a grain of truth. Take a few steps back and honestly consider what they wrote. At the same time, take an honest look at their performance as well. Their performance level can give you a good deal of insight into their credibility as well as their motivation to write the letter.
It will also help to meet with them to learn more about the specifics of whatever has caused them to become so upset. This should be an open meeting to clear the air and come to an agreement over the steps that all of you will take to improve the working relationship.
A separate matter is the action your manager took. Rather than instantly concluding that you are the problem, he should have investigated the situation and based his conclusion on facts. This is actually something you should discuss with him. If this type of behavior is typical of his style, it is possible that some letters have been written to his manager, too.