We use molecular dynamics simulations to study the effects of confinement on the phase behavior of a water-like monatomic liquid that exhibits a liquid-liquid phase transition (LLPT) and a liquid-liquid critical point (LLCP). The liquid is confined between parallel walls and we focus on the effects of wall separation and surface chemistry (solvophobicity/solvophilicity) on the location of the LLCP, temperature of maximum density (TMD) line, and loci of compressibility maxima (CM). It is found that, independently of the surface solvophobicity/solvophilicity, the LLCP, TMD, and CM lines shift rapidly towards higher pressures and lower temperatures as the wall separation is reduced. It follows that the effects of confinement on the TMD and CM lines are indicative of the confinement effects on the LLCP/LLPT. Confinement effects are observable already when the liquid particles form ≈15 layers between the walls. For the case of water, this corresponds to a separation of ≈4-5 nm between the surfaces, larger than the confining dimension of the nanopores commonly used to study the hypothesized LLPT in confined water. Hence, our results suggest that such experiments should not be interpreted in terms of the phase diagrams proposed for bulk water.