Sam Allardyce’s team headed into the Premier League game at the King Power Stadium on the back of a 1-0 win against Sunderland and were expected by many to pick up all three points.
However, it was relegation-threatened Leicester who won the contest, getting the better of the London outfit 2-1.
The hosts took the lead through Esteban Cambiasso's superb 20-yard left-footed strike just 12 minutes into the encounter.
Although Kouyate restored parity for West Ham just past the half-hour mark, substitute Andy King scored the winner four minutes before the full-time whistle.
“Leicester were giving it everything and attacking and attacking,” Kouyate, 25, told West Ham’s official website.
“They were playing with four or five strikers, three defenders and two midfielders, so they took a chance. This is football and on Saturday Leicester won.”
Leicester were desperate to win against West Ham on Saturday as they needed the three points in their fight for survival.
Over the course of the 90 minutes, Nigel Pearson’s side had 50% of the possession, took 20 shots of which seven were on target, and earned seven corners.
West Ham had 50% of the possession, took 14 shots of which seven were on target, and earned six corners.
The Hammers are currently ninth in the Premier League table with 42 points from 31 matches and will face Stoke City at home on Saturday.