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The Kagome lattice series AV₃Sb₅ (A = K, Rb, Cs) presents a variety of intriguing properties such as superconductivity, charge density wave (CDW), and a non-trivial electronic topology. Recently, a non-monotonous pressure dependence of T_c in CsV₃Sb₅ suggested an unusual competition between CDW order and superconductivity. On high quality single crystal samples, we have explored the effect of disorder induced by proton irradiation on the CDW and superconducting states of CsV₃Sb₅. Resistivity and magnetization on pristine sample exhibit two clear signatures at T_CDW ~94 K and at T_C∼3.5 K. With increasing disorder both the CDW transition and superconducting transition are suppressed. Interestingly, with complete suppression of the CDW, T_c is reduced to ~1.8 K. This is unexpected in a scenario where CDW order and superconductivity compete for the same electronic density of states as arises for instance in cuprate and dichalcogenide superconductors or in Lu₅Ir₄Si₁₀. Our experimental findings indicate significant anisotropy of the˜ superconducting gap and that the detrimental effect of CDW order on superconductivity is not as strong as previously seen in other systems.