This answer is an attempt to answer the actual question posed. Please keep in mind that this applies specifically to the Equifax credit model that Mint uses as mentioned in the accepted answer, and that different models may react in different ways (or not at all).
As mentioned in the comments, the number of total accounts you have does not have much bearing on your overall credit score. If you click on Mint's "About Total Accounts" link, you get the following statement:
Total Accounts has a low impact on your score.
Second, the way the Total Accounts score is represented is misleading. This is not a count of the total number of accounts you have open, but rather how many accounts you have in your total history. Mint's header under this metric is flat out wrong:
Try to have a good mix of credit lines open.
To back up the assertion that this is looking at total accounts in your credit history rather than just those that are open, my Mint report shows 2 open accounts and 7 closed accounts, for a total of 9. Under the Total Accounts metric, I am plotted smack dab in the middle of the "Not Bad" range, right where people with 9 would be plotted.
So the proper advice here is to just let it be and only open new accounts as you need them. As you amass credit history, this metric will continue to grow naturally - it should never decrease.
You may ask, then, why did your overall score decrease when you paid off your student loans? Most likely because your average age of credit dropped when you closed your loan account. If you're like most people I know, your student loan is one of your oldest accounts, so closing that account will hurt your score - credit age is measured only on your open accounts.