Rayan’s goal eight minutes after half time was the difference between the two sides after both were reduced to ten men in the first half.
The three points saw Bournemouth move to 55 points from their 36 games, as they remain in sixth with two games left to play.
Reflecting on the game, Iraola told the Daily Echo: “A massive result for us.
“I think also considering the opponent how difficult it is to win here, how the game has gone.
(Image: Ben Whitley/PA Wire)
“Because there is a moment when you receive the first red card where you see it as very difficult, but we kept fighting and I’m very happy for the players because they’ve shown big spirit.”
The Cherries’ Ryan Christie was the first to be handed his marching orders, for a challenge on Timothy Castagne five minutes before the interval.
But Joachim Andersen was sent off in first half stoppage time as Fulham were unable to make the most of their man advantage.
Iraola said it was a different game in the second half.
“I think we spoke during the halftime, second half was about the soul of the team because it’s 10 against 10, spaces everywhere, one against one duels, tired legs for sure at the end,” he said.
(Image: Ben Whitley/PA Wire)
“You need the soul when you are running out of energy, the subs and I think we’ve shown this. It’s true that at the end they also had especially the last chance [where Josh King hit the bar]. But luckily for us, we finished the job.”
It was an impressive defensive performance after the Rayan goal, as Bournemouth limited their hosts to few chances across the second half.
Iraola was pleased with how his side defended: “It’s a clean sheet against a very good team.
“I think considering, you know, you were playing against them 10 against 10, that is always more open.
“I think we were quite compact and the big chance they’ve had comes, I think, from a long throw. And I think overall, I think we’ve been very, very solid.”