X-ray observations of galaxy clusters are impacted by the presence of active galactic nuclei (AGN) in a manner that is challenging to quantify, leading to biases in the detection and measurement of cluster properties for both astrophysics and cosmological applications. Using automated X-ray pipeline techniques, we introduce a new automated class for AGN-contaminated (AC) clusters in the XXL source detection software. The majority of these systems are otherwise missed by current X-ray cluster detection methods. The AC selection is also effective at distinguishing AGN and cool core presence using supplementary optical and infrared information. We present 33 AC objects, consisting of 25 clusters in the redshift range, $0.14 \leq z \leq 1.03$, and 8 other sources with significantly peaked central emission based on X-ray observations. Six of these are new confirmed clusters. We compute the missed fraction of the XXL survey, defined as the fraction of genuine clusters that are undetected due to their centrally peaked X-ray profiles. We report seven undetected AC clusters above $z > 0.6$, in the range where X-ray cluster detection efficiency drops significantly. The missed fraction is estimated to be at the level of $5\%$ for the 50 square degree XXL area. The impact on cosmological estimates from missed clusters is negligible for XXL, but produces a $\sim 3\sigma$ tension with the fiducial cosmology when considering larger survey areas. This work demonstrates the first systematic attempt to quantify the percentage of missed clusters in X-ray surveys as a result of central AGN contamination. Looking towards surveys such as eROSITA and Athena, larger areas and increased sensitivity will significantly enhance cluster detection, therefore robust methods for characterising AGN contamination will be crucial for precise cluster cosmology, particularly in the redshift $z > 1$ regime.