I had crowns put on my incisors. I feel the back of the crowns with my tongue constantly! Should it be like this?

Thank you for your question.  I am assuming you were in custom temporaries while your porcelain crowns were being fabricated in which case the "feel factor" will be different from the temporary material to the porcelain.  Note how long you have had the crowns cemented.  One week or two may take some adjusting but several weeks in, you should consult again with your dentist.  Make a note if the crowns are all porcelain or if a porcelain to metal interface was utilized on the "back" side of your crowns - your dentist will know.  The tongue can discern these differences in which case polishing can help alleviate any discomfort.  Consult with your dentist accordingly and rest assured they can utilize several techniques to help calibrate your comfort and concerns.

There may be two things that are causing you to be bothered when your tongue touches the crowns. First, the crowns may be bulky or over contoured. If this is the case your dentist may be able to thin the crowns to a more normal contour. Secondly, you may be feeling the difference between porcelain and natural tooth structure. Usually the dentist can polish the back of the crown so that they feel slicker. If your dentist did adjust the porcelain and didn't polish it afterwards that could be part of your problem. If none of these work your dentist may need to make them out of a different material, one that doesn't irritate your tongue.