Brentford scored the opener through Keane Lewis-Potter in the first half and looked good value for their lead.
Yehor Yarmoliuk's red card just ahead of the break completely changed the game, however, allowing Liverpool to come back and secure a valuable three points.
Speaking to Sky Sports after the game, Iraola was happy with the performance, but admitted he wants more from his side.
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"There was a lot of things happening during the game. The first half more or less was quite level, we had the clear chances," he said.
"They scored before the end, and in the second half we needed the comeback. I think we played really well until the 2-1. After that, we started to protect something; I think we didn't manage the last minutes well.
"I think some of the players were seeing quite clear chances to finish the game that we haven't been able to finish. We lacked some composure on the ball. Sometimes it was just about keeping the ball more and not going for the goal with the first chance."
On the penalty and red card: "Two decisions, I need to see them, both of them. I think the penalty is probably not a penalty."
On Jeremie Frimpong: "He finished cramping the other day in the Champions League so we knew he wouldn't start the game. We were playing against 10, and I thought he was going to give us more going forward, but he felt straight away something in the muscle."
On Dominik Szoboszlai: "He has tried, he has trained the last few days, but we didn't know the minutes he'd have. It's not another injury, he's still not healed."