You do unfortunately. If the payoff was calculated to low and the actual payoff is higher to your current lender, that is your debt and you need to cover it. If you haven’t closed yet you can also have your lender possibly increase your new loan size to cover this difference.
I assume your loan is closed and funded since you mention that the attorney miscalculated your payoff amount. Most likely, the payoff posted at your old lender a day or so after expected, and the charge is minimal. IF the payoff was credited late, question to ask closing attorney or title company is WHY it was late. If the party responsible for sending it forgot, sent to the wrong address, or basically made a mistake, I’d be asking them about covering any shortage. IF your old lender gave them a payoff and they forwarded the amount shown in a timely fashion, title company/attorney are not at fault. One thing to remember is that your old lender MAY have rejected the payoff, meaning interest is still accruing daily on your old (potentially not paid off) loan. Need to find out ASAP if your old lender accepted the payoff and applied those funds to your old loan, or if they rejected it and you’re in never never land.