The Cherries won the fourth round tie 2-0 via Antoine Semenyo (penalty) and Daniel Jebbison.
“I think in the cup competitions, obviously the most important thing is to go to the next round, to be in the draw,” said Iraola.
“But overall the performance I think has been very good. Probably different halves.
“I think we were better in the first half. We played, I think, on the ball and with our press quite well and we had good chances. We scored the goals and probably was the moment where we made the difference.
“Second half was completely different. I think they pushed us much more. I think we had to be more in a low block for more time and I think in a different way, probably not playing as well as in the first half, but we competed well.”
On their quick start, the manager also said: “I think we normally try, especially away from home, to start strong and to be quite brave and go for the game because I think it's good if the game opens for us and we try to play as fast as possible.
“I think when you have also fresh legs, it's always easier. And in the second half we couldn't find these moments of more calm on the ball, of more transitions. I think Everton went a little bit more direct and we had to defend differently and I think we finished the game quite well.
“It's true that we had especially that play when they hit both posts and you have your little luck on your side that helps you. But I'm happy, I think we look quite solid considering how they pressed us.”