Conor Gallagher scored the game's only goal when he drove through a crowded box early in the first half.
Basham said: "If you look at the first 10 or 15 minutes we started really well. We did really well again in the second half. We are disappointed as it was a massive game. We have let ourselves and the fans down.
"We had some great opportunities to score tonight and had some great chances. We worked on it in training but it's just that composure on the main stage.
"We are hurting when we don't get results. We are used to winning games but we are playing in the Premier League against the best teams in the world. The performances are still good. We are just kicking ourselves in the dressing room today.
"It's a situation that we needed to do [bring on lots of strikers]. The lads up front were brilliant without putting the ball in the back of the net."