The Ghana international was on the scoresheet, his fourth league goal for the club and third strike in four matches since returning from this year’s Africa Cup of Nations, but was unable to save the Hammers from a 3-2 reversal.
Manuel Lanzini fetched West Ham's other consolation, while Riyad Mahrez, Robert Huth and Jamie Vardy ensured three points for the away side.
"We are very, very disappointed," Ayew said, as reported by his club's official website.
'I think we didn't get into the game when we had to and Leicester scored three goals out of nothing really.
"Two set pieces and once cross have led to the three goals, but we had chances to get back into the game and we didn't.
"We need to go back, learn from our mistakes and be better for our next game away at Hull."
West Ham find themselves on the 12th position, ahead of the Hull fixture after the upcoming international break.
"There have been games where we have conceded goals in the first ten or 15 minutes and we need to work on that and change it, because conceding early changes the whole game," Ayew added.
"We had positive things, but when you don't win, you [don't] see them. The fans were behind us the whole game and helped us to push and try to get back into it.
"We had chances and we need to work on our play in the two boxes, offensively and defensively, and hopefully we can start winning games."
Ayew joined West Ham on a club record transfer from Swansea City last sammer, penning a three-year deal worth £20.5 million.