Iraola saw his side fall to a second straight defeat without scoring despite finding the net in the fourth minute.
Antoine Semenyo thought he had opened the scoring, only to see his effort chalked off for offside following a VAR review.
Bournemouth could not stop Luis Diaz from netting a quickfire brace before Darwin Nunez got on the scoresheet to condemn the Cherries to their first away defeat of the Premier League season.
Iraola reveals "misunderstanding" with referee
Not only was it a disappointing day on the pitch, but it was also a frustrating one on the touchline after Iraola picked up a costly yellow card.
After previously being booked against Newcastle United and Chelsea, Iraola is now set to receive a touchline ban for reaching three yellow cards for the season.
However, the Bournemouth boss feels he was hard one by in Saturday's clash at Anfield, claiming that their had been a "misunderstanding" with referee Tony Harrington.
"There has been a misunderstanding," Iraola told BBC Sport after the game "They booked me because I asked for a yellow card, and I was asking just for offside.
"They [the players] haven't done one foul, nothing, to ask for a yellow card. He told me: 'You cannot ask for a yellow card'.
"I asked for an offside because he doesn't go for the ball but after he goes to press, Darwin, from the offside position, and we have to play back to the keeper.
"I think the referee doesn't want to stop it, he leaves it go, but it is bad for us, you know? It's not an advantage for us and I was asking: 'No, no, it's offside, give us the offside', that's what I was asking.
"He told me straight away: 'You cannot ask for a yellow card'. I know, already, I have paid my price in the season before, I know I cannot do this, but I hope we can overturn it."
Iraola faces touchline ban
While Iraola wants to overturn the booking, he is currently set to be banned from the dugout for next weekend's meeting against fellow South Coast side Southampton.
Bournemouth will head into the upcoming home fixture in 13th place, having won one, drawn two and lost two of their five league matches this season.