Can non-payroll contributions to HSA be tax-exempt?

I do not have payroll deductions set up to contribute into my HD health insurance's HSA (health spending account).  However, I have had expenses this year (and the last 2 years) that qualified as expenses exceeding what monies my insurance contributed into the HSA.  If I make my own contributions this year with after-tax funds, can I get credit for these as tax-free when filing my taxes?

The insurance company's (Aetna) bank that  manages this debit card (JP Morgan) stated I could add contributions on my own up to the year I first had this account (2012) and use them to 'refund' myself for expenses in these last few years.  However, they would not tell me if this would overall reduce my taxable income when filing this coming year.  Please advise.  Thank you.