The Cherries triumphed 1-0 thanks to David Brooks' winner.
Iraola said: “We really deserve this one.
“I think we were controlling the game since the beginning.
“We knew that against Everton it’s difficult to score because they have a good keeper, good centre backs, even if you push them and they can feel a little bit the pressure, they are a good defensive team and we had the patience.
“Probably we should have scored earlier but it didn't happen until the end. But I think everyone watching the game was feeling that the goal was coming.”
On Brooks' winner, the Basque continued: “I think it has been a lovely goal.
“Everything, how we found the space for Milos (Kerkez), the cross in, the composure of Brooksy, the striking of the ball.
“I think everyone sees the goal and feels like he wanted to put the ball exactly where he puts it.
“And he also had another very similar chance, straight away and he almost scored another one and I'm happy for all.”