Liverpool claimed a hard-fought third Premier League win of the season at nine-man Brentford thanks to second-half goals from Víctor Muñoz and Alexander Isak.
Keane Lewis-Potter had given the hosts the lead in the first half before Yehor Yarmoliuk was sent off for a headbutt on Jérémy Jacquet. Vitaly Janelt was later sent off for a second bookable offence at the end of the second half.
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The Reds came into the game having beaten LASK 6-3 in the Champions League in Austria on Wednesday night.
Iraola will have been hoping the victory could provide a boost to some of his previously misfiring attacking players, with new signing Bradley Barcola scoring a hat trick -- his first goals for the club -- and Florian Wirtz also looking much-improved, albeit against significantly weaker opposition.
"I'm really happy for Bradley because you were asking me yesterday about him not making the numbers, also Florian [Wirtz]," Iraola said after the game against LASK.
"I think both of them today played really well. I think they made a difference. Bradley apart from the hat trick, I think he was a threat always -- one-v-one, threatening in behind.
"Also Flo helped us a lot to control the game, finding the pockets. I'm happy for both of them.
"I think their confidence, for sure, is very good. I think they feel that we trust them a lot. But at the end, to enjoy a little bit playing in the Champions League away, I think it's going to be very good for them."
Brentford, meanwhile, came into Saturday's game in excellent form and started the day in fourth place having not previously lost a game this season.