It does create a net force on the surface molecules towards the depth of the liquid. This is the proper way to understand surface tension, better than the complicated explanations given so often. At the surface of a lake, depth means downwards, yes again.
Since the superficial molecules at North or West also get the same force, this alone doesn't curve the surface. The surface deeper at one location implies that it's higher elsewhere, negating any gain. So on a big surface, you won't notice a significant curvature.
Things change at the ends of the surface. There, it depends on how strongly the container's surface attracts water molecules: more or less than the water molecules attract an other. If the container attracts more, water climbs a little bit against the container; if not, water joins the container lower.
This effect can compete against gravity in the mm scale. Since the energy of surface tension increases as an area but gravity as a mass hence volume, at a bigger scale gravity wins. So surface tension is all-important for fog droplets and mosquitoes, but negligible for the shape of a lake.
Surface tension is more effective if the contact area increases as compared with the volume. This is the case in a capillary tube or at a wick, where capillarity can raise a liquid higher.