McKenzie, who represented Team GB at the London 2012 Olympics, recorded the best result of his career at the Europeans with -60kg bronze.
And he got off to the perfect start in Azerbaijan defeating Ukraine's Dmytro Atanov by ippon in little over a minute to set up a pool final against Ilgar Mushkiyev.
Again he secured an ippon for victory and a semi-final place however he couldn't navigate his way past Mongolian top seed Amartuvshin Dashdavaa.
That put McKenzie into a bronze medal contest with Robert Mshvidobadze of Russia but he was thrown for ippon at the death to finish fifth.
And British Judo support coach Luke Preston said: "Ashley showed another consistent performance at the very top level and was unlucky not to medal.
"Hopefully this will now be enough points for qualification for the IJF Masters in three weeks."
McKenzie wasn't alone in flying the British flag in Azerbaijan as Louise Renicks finished seventh in the -52kg category.