Barnes made a fast start and took the fight to Zou, who stepped up the pace as the first round wore on to take a three-point lead.
The Chinese fighter had preserved his advantage by the time third-round bell rang and he was keeping outside of the Irishman's reach.
However, Barnes did manage to drag him into a scrap in the final round. The pair stood toe to toe in the centre of the ring and engaged in a furious exchange, of which Barnes got the better by far.
Zou was now not moving so fluently and Barnes took full advantage, landing a string of heavy shots that took the life out of the Chinese man's legs.
A terrific final round from the Irishman was not enough to see him advance, as Zou was awarded the victory on countback after the judges scored the contest 15-15.