No, you cannot get HIV that way. HIV is not easy to contract and the virus must enter your bloodstream. Any minor pricks, scrapes, and cuts can be ignored, because they do not allow sufficient pathway for the virus to enter your bloodstream.
This is why the only injection risk is from a re-used needle, with a syringe attached, that keeps blood in a vacuum (the syringe), which can then be injected into a vein. You had zero risk from a lancet prick.