Each component has different weights: https://www.myfico.com/credit-education/whats-in-your-credit-score

So when you paid off your student loans, two components in the score were probably negatively affected: length of history and credit type mix.

It's likely that the student loan was one of your longest running accounts. So paying that off could bring the average age of your existing accounts way.
And if the student loan was your only no-credit card type of debt, then your score will be negatively affected after paying it off since you no longer have installment loans on your history.

It's a dumb system, but that's just the way it is. But I wouldn't worry about it unless you have immediate plans to get new credit (car loan, mortgage). You score will eventually go back up if you keep doing the right things.