The progenitors of many fast X-ray transients (FXTs) and those of $\gamma$-ray bursts (GRBs) are strongly linked. Given that `dark' GRBs are typically found to be events suffering from enhanced extinction in the host galaxy, we investigate the nature of `dark' FXTs. However, unlike $\gamma$-rays, soft X-rays are strongly affected by absorption, implying that dark FXTs discovered by Einstein Probe's Wide-field X-ray Telescope (EP-WXT) have to be emitted at energies >2--3 keV rest frame hence at a redshift $z\gtrsim 2$. To illustrate this, we present two dark FXTs, EP241103a and EP260409a, discovered by EP-WXT. For EP241103a, the high extinction precluded the detection of the optical counterpart, while for a probable source redshift of $\approx 2.5$, the rest-frame X-ray photons are not severely affected. For EP260409a no counterpart is detected in the optical, but we do detect a near-infrared counterpart. A plausible scenario for EP260409a is that it lies at a redshift $z \gtrsim 4$. Additionally, we conduct simulations of FXTs observed with EP-WXT, showing that the detected counts for absorbed events ($N_{\mathrm{H}}\gtrsim 10^{22}$ cm$^{-2}$) strongly decrease at low redshifts, hindering their detection. These results support the theoretical prediction that dark FXTs have an intermediate to high redshift and a different selection function from those of dark GRBs.