Rio Ngumoha's deflected second-half strike proved the difference.
"I think overall we were more solid than the other day. It was a different kind of game, the pitch is quite narrow and there are not a lot of spaces. But I think we had good spells. And even if the other day maybe you score more goals and it looks nicer, I think today we were more a team and more collective," Iraola said.
The Spaniard, who replaced Arne Slot as head coach this summer, fielded a youthful side missing Ryan Gravenberch, Florian Wirtz and Alexander Isak, all of whom only reported for pre-season training on Sunday and are being eased in gradually. Iraola was pleased with how several fringe players responded to the test.
"I'm happy today because we played a lot of the young players. Some of them had difficult match-ups, [Luke] Chambers playing as a centre-back against big bodies, he covered very well and played very well from the back. The wingers – Josh Abe, Kieran Morrison at the end. Good performances from young players, which I think is always good," he said.
He also praised Lewis Koumas and Will Wright for helping the team both in and out of possession, saying both had "done a very good job today," working the press and linking play with Harvey Elliott and Dominik Szoboszlai further forward.
Asked how far his side is from developing his preferred identity, Iraola pointed to gradual progress rather than a finished product.
"I think we're still not there. We are sometimes arriving late, but I think it's a step forward, since especially the first half against Sunderland. That is more of a reference than the second half. Slowly, slowly I hope every game we are closer and closer. We start to add new bodies, because now we are playing with a lot of the young players. Slowly, slowly we have to add the senior players that are starting to train with us, so we can arrive to the beginning of the season in a good place," he said.
Iraola singled out midfielder Trey Nyoni for special praise.
"Trey is very good on the ball, very calm, he reads the situations well. We're forcing him in the work without the ball, in the press, and he is absolutely doing very well. I think the timings of the jumps are very good. He is always confident on the ball so we encourage him. Sometimes even if he loses the ball, 'Try to find the No.10, try to find the No.9, even balls in behind, look a little bit further' because he can do it, because he is so good," he said.
Gravenberch, Wirtz, Isak and Jeremy Jacquet are expected to have their first pre-season minutes against Leeds on Sunday, Iraola confirmed, as Liverpool continue integrating their senior players ahead of the new campaign.