Alexander Isak and Florian Wirtz put the Reds on track, but just like against Leeds last week in Chicago - when they were also two goals up and lost 4-2 - they were unable to kick on.
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Aleksandr Golovin's penalty and Mika Biereth got Monaco back level, before Paris Brunner headed in a late winner.
But minutes in the tank were clearly the priority for Iraola, who made 11 changes to his side in the second half, and handed a first Liverpool appearance for new signing Victor Munoz.
The key moments from Anfield...
7: GREAT SAVE! Hradecky called into action to deny Wirtz! He dives low to his left to keep out the German's bending strike after good footwork from Isak to tee him up.
16: GOAL! Isak off the mark at Anfield! A lovely move on the edge of the box as Gravenberch plays a one-two with Szoboszlai and then touches it into the path of the Swedish striker. He then turns and rolls it bottom corner.
29: GOAL! Liverpool are cruising. A ball into the area from Koumas leads to an absolute scramble in the six-yard box after Gakpo heads it back into the melee. Wirtz then pokes in from two yards.
43: PENALTY TO MONACO! Golovin charges into the box and steps past Van Dijk before being brought down just inside! The referee points to the spot...
44: GOAL! Alisson goes the right way to his left, but Golovin's penalty is too good for him, high into the net. Monaco have one back!
56: GOAL! Monaco have levelled up! Biereth gets into the box and see his first effort saved by Mamardashvili. But it breaks back to the forward and he slots it home.
61: SUB! Victor Munoz gets a huge cheer as his name is announced at Anfield for his first appearance as a substitute.
70: BIG SAVE! Monaco are pushing to take the lead! They work it left and the ball comes into the box for Coulibaly to have a pop. He hits it lovely, but Mamardashvili gets his hands on it to push it away.
88: GOAL! Lovely corner whipped in and Brunner rises at the near post to head in! Monaco have come from two goals down to take the lead at Anfield.
Liverpool's pre-season so far...
July 25: Liverpool 4-2 Sunderland - Nashville
July 30: Liverpool 1-0 Wrexham - New York
August 2: Liverpool 2-4 Leeds - Chicago
August 9: Liverpool 2-3 Monaco - Anfield
August 16: Liverpool vs Como - Anfield, 6pm
