You are actually facing two problems in this situation, and they both have the title of manager. First, having someone who is not your manager launch a barrage of potshots is totally unacceptable, especially where there is no substantiation. If another manager is concerned about your performance, he should discuss it with your manager.
Speaking of which, your own manager does not understand the importance of responsiveness and communication in the managerial process. His lack of action in this matter is actually providing the criticizing manager with a green light.
If you are certain that the criticizing manager's comments are totally inaccurate, you should meet with him and provide him with the facts. The tone of the meeting should be cordial and businesslike, and the stated objective should be to clarify some points that may be causing dissatisfaction and confusion.
Let your own manager know about the steps you have taken. If the problem persists, the next step is to meet with both of them at the same time. Their reaction and follow-up actions will help you determine what to do next.
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