Danny Welbeck’s 42nd-minute effort ensured Arsene Wenger’s men secured passage to the semi-finals of the competition.
And the Ghana international who made his 18th appearance for the Hammers this term is frustrated they could not make their fans happy.
"We’re quite disappointed to be out of the cup because I think we could have gone a step further,” Ayew told West Ham United Website.
“The fans were unbelievable. My friends, they sent me a message afterwards saying West Ham fans are on fire!
“I’m disappointed we couldn’t make them happy like we did at Wembley, but we want to thank them for coming and for their support. We’re going to keep running and playing and trying to give them a better football to make them happy.”
“Arsenal had more possession and played the game, but we defended well and they didn’t really have any clear, clear chances. I think they got the one where they scored but in the second half, there was no clear chance.
“We didn’t manage to play our game or come out with the ball on the ground from the back, but there are things that are positive but also negative things we need to work on to be better in the league.
“We’re going to use this game to become better and work and be better for Saturday because that’s what important at the moment.
“I think we have players who have the desire, players who want to run and play for the Club. We are getting better and better. We lose maybe 1-0 at the Emirates, with young lads also playing, it’s good for them, it’s good for the Club, for the future.
“Like I said, I’m disappointed because I’m a competitor and I always want to go further, but I think we can learn a lot from this and we can become a better squad and hopefully we can get good results before the end of the year.”
Ayew who has registered five goals this season will be looking to help West Ham put the defeat behind them when Newcastle United come visiting the London Stadium on Saturday for an English Premier League fixture.