First-half goals from Cody Gakpo and debutant Jeremy Jacquet secured victory in the second of two meetings between the sides on Sunday, following a goalless draw earlier in the day at the AXA Training Centre.
Iraola felt the clean sheet and the result carried more significance than the performance itself, with his side settling for game management once the lead had been established.
"I think we need a little bit this feeling of finishing with a clean sheet, winning the game," Iraola told Liverpoolfc.com.
"Still, the first half has been better than the second, but at least we kept our organisation, our composure and we found a way to finish with a clean sheet, 2-0. I think we needed this feeling before we start."
Jacquet was one of two new faces given their first outing for the club, alongside centre-back Ronald Araujo, and Iraola was encouraged by both performances.
"Yes, both of them. I think Jeremy played really well. Also Ronald played really well when he came in. When you have two new faces, first game for both, they do so well," he said.
The manager also singled out Jeremie Frimpong's display at right-back across the full 90 minutes, praising his ability to contribute going forward while remaining solid defensively.
On the physical condition of his squad with the Premier League opener at Newcastle United fast approaching, Iraola struck a cautiously positive tone.
"I think we are better than we were last week. Still, I hope next week we are better than we were today," he said, noting that several players managed 80 or 90 minutes without picking up injuries. "It's keep building these fitness levels, this also [mentality] even when you are not as fresh [to] keep the focus so you don't make the big mistakes. I think it's an improvement but still – especially second half – we need to be better."
Liverpool now have close to three full weeks to work with before their opening two league fixtures, against Newcastle and then Ipswich Town, and Iraola intends to use the time to build understanding between his squad's new arrivals and the rest of the group.
"We need training, we need to train together. Some of the players that have started playing today, we need to build relationships, the players to have this option to solve problems by themselves in the pitch," he explained.
The head coach also praised his squad's response to a change in approach out of possession.
"I'm very happy with the attitude of the players. They are training really well. I am asking them to do things that are a little bit different – especially without the ball – and I think they are trying to get it," he said. "Obviously now still we are not perfect. We have things to improve but I'm very happy with their attitude, their willingness to be on the same page, and we will get there."