Slaven Bilic’s side surrendered their one-goal advantage to the Clarets courtesy of Chris Wood's header with five minutes left to play.
And the 27-year-old midfielder has recognised the impact of the 3000 Hammers support who made the trip to Turf Moor and thanked them for their unwavering support throughout the game.
“This is not a surprise. We have the best fans in England, you know, and everywhere we go the fans are coming and making noise for the team," Kouyate told club website.
“They’ve just got to continue that for the next game.
“We were winning 1-0 until the 85th minute and then took a goal, which was very hard for us.
“We are so angry because it’s possible to take three points from this game, but we took one point.
“This is football, though, so we just have to concentrate on the next game because we need to take a lot of points,” he concluded.