Visual assessment of soil structure receives growing interest but its physical meaning is still to be explored. This study examined the relationships between soil pore systems volume and size distribution and visual structure quality scores in undisturbed soil samples from Swiss cropland soils covering a wide range of soil organic carbon (SOC) and clay contents. Structure quality scores were determined with CoreVESS. The pore system volumes were quantified by shrinkage analysis, and the water retention curves were used to determine the equivalent pore‐size distribution. CoreVESS scores showed non‐linear relationships with total and structural pore volumes. They correlated mainly to structural porosity volume, whereas plasma pores did not explain structure quality scores. As a result, the total porosity was less correlated to CoreVESS than structural porosity. The small‐size (< 50–100 μm equivalent diameter) structural pore volume showed the higher correlation to structure quality score. The small‐size structural pore volume was mostly correlated with the SOC:clay ratio and, to a lesser extent, with SOC, highlighting the link between soil structure quality and clay‐SOC complexation in these soils. Soils with SOC:clay ratios above 0.1 showed significantly larger volumes of small structural pores. Our findings underline the functional importance of these small‐size structural pores, which are also accounting for air‐water equilibrium close to field capacity, and were pointed out for their role as soil biota habitat. Their tight relationship with SOC suggests a good stability upon stresses and slow changes over time. In contrast, large structural pores, which are known to be sensitive to mechanical stress of soil fauna activity, were primarily influenced by carbonate content.