The Reds boss is just a couple of months into a two-year contract signed to succeed Arne Slot, and arrives during a period of significant upheaval both on and off the pitch.
Owners Fenway Sports Group have agreed to sell 38% of the club to Amit Bhatia's 1892 Holdings consortium, which includes the world's third-richest man, Jeff Bezos, and Facebook co-founder Eduardo Saverin.
FSG's chief executive of football, Michael Edwards, stepped down earlier in the summer, while sporting director Richard Hughes is expected to join Saudi Pro League side Al-Hilal once the transfer window closes.
On the pitch, Liverpool have lost Mohamed Salah, Andy Robertson and Ibrahima Konaté since the end of last season, and Curtis Jones followed them out of the door this week in a £30m move to Inter Milan. That level of turnover has left few pundits tipping Liverpool as genuine title challengers this season, but Iraola believes his squad's quality is being overlooked.
"Yes, I can feel a little bit [that people underestimate us]," the 44-year-old said. "Because of the questions you ask me. We have to value the good players we have.
"Sometimes the players are here for three or four seasons and we are not aware how good some of our players are. I know this is the situation. The market is not closed, still we have more time to add players.
"Probably we have the advantage that I am not new and I value a lot of the players I have here. I can tell you that I am very confident in terms of the quality of the players I have. [Pre-season] has confirmed what I expected from most of the players. You enjoy being part of the training and seeing them perform well.
"Probably, a little bit of this negativity is about the fact we have a tricky situation with long-term injuries. We have four very good players who had big surgeries — Hugo Ekitike, Conor Bradley, Giovanni Leoni, Wataru Endo — that are very good players. If they are available it puts you and your squad in a much better place. We have to go through this period until they are fully fit. We knew it from the beginning and I hope we can deal with this time."
Iraola added: "I want to think we are in a place where although we are not 100% but we can still start well. I think we are at a level where we can be very competitive from the beginning. Definitely we have to improve. But, even if we win the first game, we will need to improve.
"You are right that it took some time in Bournemouth to get everything clicking but I hope it takes less time. Even if not 100%, we can be competitive and get results before."