The Cherries were well worth the points which came through goals from Eli Junior Kroupi and Alex Scott.
Iraola said afterwards: "We showed great personality to play in a big game and a big stadium. We've been at the level of the game. I'm very happy for the players."
On 22 days without a game before today, he continued: "You are worried you lose the intensity of the competition. We started really well. We recovered some players. Physically we sustained the level of the game. We finished strong. We were coming from a lot of draws in a row.
"Alex (Scott) has been like this for many months. He was amazing today. He's in such good form. I'm so happy for him. He's worked a lot to be at this level.
"Defensively apart from the penalty we defended those (set-piece) situations. We were quite brave. A complete performance.
"It's a matter of growing into the game. We had very good spells on the ball. We were finding good gaps in the middle."
The win takes Bournemouth into ninth place, four points outside the European places.
On their European hopes, Iraola concluded : "It's difficult for us but it's true that we are not far. There are many teams in a good run without losing. Whoever gets the final two spots will finish in a big run of games."