An ink pressure regulator for regulating a hydrostatic pressure of ink supplied to an inkjet printhead. The regulator includes an ink chamber having an ink outlet for fluid communication with the printhead via an ink line. A roof of the ink chamber includes: an air inlet; a regulator channel having a first end communicating with the air inlet and a second end communicating with a headspace of the chamber; and a liquid-retaining structure in fluid communication with the regulator channel. The liquid-retaining structure is positioned and configured for capturing ink from the headspace of the ink chamber. The regulator channel is dimensioned to regulate a hydrostatic pressure of the ink supplied to the printhead.