We propose a new measure, the Implied Correlation Gap (ICG), to quantify the degree of the inadequacy of implied correlation to capture implied market dependence. We define ICG as the ratio between the implied correlation and an alternative implied dependence measure that captures both linear and nonlinear dependence. Both theoretically and empirically, we show that the ICG is driven by the dependence information which implied correlation fails to capture. We show that correlation is only an adequate measure for market dependence in case the joint return distribution is described by the Black & Scholes model. The more the market implied distributions deviate from the Black & Scholes model, the higher the ICG is, indicating the deterioration of the implied correlation as a gauge for market dependence. Besides, we also document that the ICG significantly forecasts cross sectional return dispersion, implied market volatility and idiosyncratic volatility.