The answer to this question is always “no”. Uncategorically. In some cases, there is no real problem and it is just the cement that holds the dental crown in place that has been dissolved or otherwise compromised, but the problem is, you need a trained medical professional to be able to determine why and how the dental crown fell off. But the crown may be damaged, the tooth may have decayed, and you may not be able to re-adhere the dental crown without causing damage. The best thing to do in these cases is to wait it out until you can go back to your dentist and get the dental crown put back by a professional.
What went wrong
It doesn’t matter if the dental crown is damaged at all, or if there is any visible damage to the teeth. It doesn’t matter if the crown has been dislodged or completely removed due to trauma, or just happened to fall out. Unless you are a trained medical professional who specialises in dentistry, you will not have the proper knowledge and equipment to re-adhere, because you need to find out what is wrong with the tooth or the crown, if anything is wrong, and how to put it back to avoid damage to the periodontium, the teeth and the crowns.
What to do with a dislodged dental crown
Instead of trying to re-adhere it, here is what you should do with your dental crown, on the off chance that it has come off.
If the dental crown is not swallowed:
First call the dentist, and tell him or her what has happened. After this, book an appointment for as soon as possible. Then, make sure you carefully clean the crown off, and keep it in a sealed place where no bacteria can start to infiltrate it. Take the crown back to the dentist, and s/he may be able to put it back on.
If you have swallowed your crown:
Get an x-ray of your intestines immediately, and call the dentist for an appointment. If based on the x-ray, a doctor tells you that you will pass the crown, then there is nothing to worry about. The dentist will make a new crown for you, and will fix whatever problem it was that caused the failure of the first dental crown.