Justin Kluivert struck a hat-trick of penalties - all won by Evanilson - for Bournemouth to win on the day.
O'Neil later said: "Not good enough. It was well below the level we've managed to reach in the last four. We made it really difficult with the errors and the game became a chase.
"The start of the game, the first goal we concede, it's a big set-back. We gave away two back passes and we didn't need to play backwards in those moments.
"We expect better than that. We should be able to make simple passes and good decisions with the ball. Today it snowballed on us. We kept on giving chances and making bad decisions.
"We did keep fighting and did come back. But we again found a way to shoot ourselves in the foot with the fourth goal.
"The lads were very well-prepared for what Bournemouth were going to ask. We knew they would be direct and press. But today we didn't have the answers.
"A lot to look at, but a very quick turnaround. The Premier League you can lose momentum at any point because there are a lot of tough games.
"The players are still together and ready to go."