Hearing criticism is difficult, especially if it's from your boss. How you choose to respond to a critical email might affect your career trajectory at your employer's, your relationship with your boss and your reputation. Before you respond to your boss's email, you'll have to control your emotions so you can think clearly and avoid making a damaging mistake.
While it's easy to jump the gun and fire off an email of your own, you need to speak to your boss by phone or in person first. You can't decipher tone from an email and you don't know what was going on when it was written. For example, a short and terse email might be the result of your boss being in a hurry. Confirm the contents of the message with your boss before you formally reply, to prevent an unnecessary misunderstanding.
If the email is just as critical as you immediately thought, you need to accept and learn from it. Don't get angry at your boss if the criticism is entirely warranted. For example, if your boss is criticizing your inability to meet deadlines, you'll need to improve your system so you turn your work in on time. You'll have a hard time advancing at your current employer or may even possibly lose your job if you completely dismiss valid criticism from a superior.
Think Before Replying
If you're going to reply, think about what to say first. If the criticism is valid, thank your boss for his guidance and mention how you'll avoid repeating the same mistake and your plans for improvement. Unwarranted criticism merits a more controlled response. An angry reply won't get you anywhere with your boss, so address the criticism in a polite but honest manner. For instance, if your boss is criticizing the way you handled a particular problem and you weren't at fault, mention you weren't the one who made that call but that you will do whatever you can to ensure it doesn't happen again. You don't need to identify the employee who did make the error, however.
Read your reply before you send it or write down what you plan to say if you're replying in person. Ask yourself how the reply sounds. Do you sound angry, rude or confrontational in any way? Can anything you say be taken more than one way? Revise your reply if you answer "Yes" to any of those questions. You want to get your view across to your boss in a meaningful conversation and not an argument. You can ask someone else to review your reply before you send it, but avoid showing it to coworkers, as word may get back to your boss.