The Hammers were expected to win the Premier League clash against the relegation-threatened Foxes at the King Power Stadium, but they slumped to a 2-1 defeat.
Hosts Leicester took the lead through Esteban Cambiasso's superb 20-yard left-footed strike just 12 minutes into the game.
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.
Kouyate has now expressed his regret at failing to win and told West Ham’s official website: “I am sorry for all the supporters and I want to thank them all.
“Normally we would win this game, but on Saturday we didn’t. They supported the team fabulously, but the result was bad. We thank you and say sorry for this result.”
It is a sincere apology from a player who has given his all and done his best for West Ham this season.
In 24 Premier League appearances so far this campaign, Kouyate has scored four goals and created 14 chances, while having a pass accuracy of 80% and a shot accuracy of 52%.
West Ham are currently ninth in the Premier League table with 42 points from 31 matches.