Brooks slotted home a second-half equaliser to cancel out Matt Grimes opener at the Swansea.Com Stadium as the Wales international celebrated his first competitive goal for over two years, and first since returning from cancer treatment.
“He was the captain today, and it’s good that he scored. Like the others, he was much better second half,” said Iraola.
“He’s trying to push himself and fight for a starting place. It is good to have this kind of competition.”
A first goal for the club since his £25mmillion summer transfer from Hamed Traore then gave the Cherries the lead before Jamie Paterson tied matters up again in the 79th minute.
Just as it looked as though the second-round tie would go to penalties, Ryan Christie rounded off a sweeping move in the first of eight added minutes to clinch victory for the Premier League visitors.
“It was a game with two different halves. We started very badly and we were slow to move the ball,” said Iraola.
“The second half was different and we were much quicker, and we moved higher up the pitch. But this is the cup and sometimes you have to suffer.
“The attitude and willingness to attack the space in the second half was much better. We were more aware of the situations, and after half-time, the game was more open.”
Iraola gave a first start of the season to Wales striker Kieffer Moore before substituting him at half-time.
Moore remains a transfer target for his old club Cardiff, but Iraola says he is happy to keep him in his squad.
“The situation is the same, it depends on whom leaves the club, but the market can go until the last day,” he added.
“We are happy with Kieffer as he gives us different options. Right now, this is the situation, but it can change from one hour to another.”
While Iraola had something to celebrate, it was another defeat for new Swansea boss Michael Duff.
He said: “You don’t want to lose any game, but it would have been nice to have gone through. Ultimately, they still had to bring their big guns on to see us off.
“The strength of their bench shows the gaps have got big again. The gulf between the leagues is now as big as it was 15 years ago.
“There are loads of positives. We were really good for 25 minutes and then we defended well, too. There were other parts that were not so good and it’s about stitching the good parts together for 90 minutes.”
Duff was delighted to see Paterson claim his goal, saying “He’s never had blistering pace, but he’s a jinker, has good feet and has real quality”, and admitted goalkeeper Steven Benda is on the verge of joining Premier League side Fulham.
“It’s a deal that suits the player and the club. We know we need a few people in, but if we don’t, we don’t – we’ll just crack on,” added Duff.