The Irishman was given his marching orders for bringing down Amine Adli as he raced onto a Junior Kroupi through ball on the counterattack, and referee Andrew Madley showed no hesitation in brandishing the red card.
That came at the end of a ten-minute spell where the Cherries had been much the better side, seeing them first equalise through Rayan and then take the lead thanks to an Adli header.
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But the Toffees regained control of the match after the red card despite being down to ten, and pushed for an equaliser, although Bournemouth held them off to collect the three points.
Boss Iraola said he wasn’t pleased with how his side had reacted to the hosts going down to ten, and admitted that there was plenty for them to work on despite earning the victory.
Everton's Jake O'Brien is sent off during the Premier League match at the Hill Dickinson Stadium, Liverpool. (Image: Peter Byrne/PA Wire)
“We were playing very well until the red card, and I think it has probably simplified their game and we haven't played well,” he told the Daily Echo.
“Eleven against 10, I know, I understand that it's difficult in the sense that they don't need more to be a threat because even from [Jordan] Pickford straight away they go direct, they put the bodies in your box.
“If they win the first contact, there is always some second ball, some finish, something can happen. They've created some corners, set plays, and I haven't liked how we dealt with those minutes.
“We've defended well in that situation, but in a win, I think we have a lot of things to improve because I think from the last games, I don't want to say like the worst performance, but I think we really probably don't deserve to win today.”