Left ventricular (LV) impaired pump function is known to be associated with altered cellular mechanical behaviour. Quantitative translation from cellular properties to whole-organ cardiomyopathy phenotype is an ongoing challenge. To quantitatively map cell-level pathophysiology to whole-organ contractile function in aortic banded (AB) 6-weeks post-surgery rats, we consider an in silico model of LV hypertrophy which combines mathematical models of cellular electrophysiology and calcium dynamics, sarcomere contraction and whole-organ mechanics solved over geometries derived from control and AB rat hearts. The resulting multi-scale mathematical model is regulated by >100 parameters and is computationally expensive. To assess the impact of model input parameters (and their combinations) on model outputs we developed a computationally effective approach for global sensitivity analysis (GSA) of rat cardiac mechanics based on Gaussian process emulation (GPE). We identified 8 key parameters regulating active tension development at cellular level, cardiac tissue and haemodynamics properties, and described the LV contractile function using 12 measurements characterising the LV volume and pressure transients and the pressure-volume loop. We found the myofilament calcium sensitivity to be the most significant parameter in explaining the total variance in both the control and AB rat. Calcium unbinding rate from Troponin C and maximum cellular tension parameters yielded, respectively, the second and the third highest impact on the LV features' total variances. The GPE-based GSA approach presented here enables computationally efficient identification of key components in 3D ventricular mechanics models, a potential path towards discovering new targets for heart failure treatment.