Former Blues goalkeeper Djordje Petrovic made four saves on the day, with the Cherries matching Chelsea toe-for-toe.
Iraola told the Daily Echo afterwards: “I think everyone defensively has done his job.
“We had difficult duels. Our full backs I think have dealt quite well with their wingers. Our centre backs, they've been brave enough to sometimes jump to (Cole) Palmer, to Joao Pedro.
“And also the midfielders, Alex (Scott) and Tav (Marcus Tavernier), we know they are good on the ball.
“Probably it's not their best position but they've played really well. And I'm very happy because we looked like us, like a solid team, dangerous when we recover the ball. And I think it’s a much improved performance comparing to the Everton one.”
He added: "It’s a point, it's not a lot, but I finished really happy with the performance.
“I think we've played a really solid game. Probably we were the team closer to win it.
“Even if you have to value the point because we were facing a very good team and you always have the fear that they can score a counter or they can make a difference like they did I remember past season's game that was quite similar.”