Alexander Isak and Florian Wirtz put the hosts two goals up by the half-hour mark of Iraola's first home game in charge, but Monaco pulled one back from the penalty spot on the stroke of half-time, equalised soon after the restart, and grabbed a late winner as Paris Brunner glanced home a header from a corner.
Assessing the game, Iraola drew comparisons with a recent friendly against Leeds United.
"I think quite similar to the game we played against Leeds. I think we played really good in the first half, especially the first 30 minutes, but right now probably we don't have much more in terms of the level required to play like this," he said.
"Then they were much better in the second half, in the same way were better in the first half they were much better in the second half, and they deserved to turn around the game, yes."
Several senior players made their first appearances of the summer against Monaco, and Iraola gave a mixed assessment of his squad's condition.
"I think they were in different levels but mostly they were in a good place. I think the ones that it was their first game, or even the ones that it was their second game, they had energy," he said. "The problem is right now probably they don't have the energy for 90 minutes and they start to get tired. It will take time with them, we need more training with them. But we can take a lot of positives, but also a lot of negatives from today."
Iraola also gave a fitness update on Jeremy Jacquet and Curtis Jones, both absent on Sunday.
"Jeremy Jacquet, we were in doubt whether to put him in the squad today, we decided not but he should be fine for the next one. It is taking a little bit of time, as we expected," Iraola said. "Curtis, he has trained every day but yesterday finished with issues in the hip. It doesn't look anything big but it didn't make any sense to risk and those are the ones, more or less, closer to a return."
Asked his broader concern after four friendlies, Iraola pointed to Liverpool's inability to hold their level for 90 minutes.
"I think we are, right now, especially considering we won the first two games but the last two, we cannot sustain the level that we want for all the game," he said. "As soon as we have made some changes they start to get tired, we cannot sustain that level, so we have work to do."
Despite the result, Iraola praised the Anfield reception on his first outing as head coach.
"Yeah, lovely, lovely - especially in the first half when we were pushing and everything was going so well, we were enjoying it," he said. "The second half has been harsh because when they are expecting you to go and you are not able, and you cannot give them what we wanted, it is frustrating, yes."
Liverpool's pre-season continues before Iraola's competitive bow away to Newcastle United on the opening weekend of the Premier League season.