I was horrified to see that an online dictionary is now even mentioning the word drug as a non-standard past tense conjugation of the word drag instead of what it is, which is substandard. I haven’t checked to see whether the latest print dictionaries have followed suit, but if they haven’t yet, I’m sure that they will. This is an excellent illustration of the dictionary being a wonderful reflection of current word usage but not necessarily a wonderful reflection of correct word usage.
Drag is what is called a regular verb. A regular verb follows a specific pattern of conjugation when making the past tense: you simply add ed to the root word. In some cases, of course, you have to double the consonant before adding the ed; in other cases, you only have to add d because the verb already furnishes you with the final e; and in still other cases, you have to change the y to i before adding the ed, but these are all part of the “regular verbs add ed to make the past tense” rule.
Again, drag is a regular verb; therefore, the past tense is dragged, and no amount of incorrectly using drug as the past tense is going to change that. When I was growing up, drug was considered to be substandard grammar–and no matter how many dictionary review boards want to encourage its use by upgrading it to non-standard in modern dictionaries because some people don’t practice good grammar, that’s what it will always be, which means that you should NEVER use it—not under any circumstances and not even in casual conversation—ever.