A disjointed Matildas side fluffed their lines in front of goal at McDonald Jones Stadium, while Alice Soto threaded the ball beautifully to help Diana Ordonez nab the match-winner.
World rankings would have suggested victory was a lock for a full-strength Matildas outfit, with Montemurro welcoming Steph Catley, Emily van Egmond, Mary Fowler and Ellie Carpenter back to the starting line-up for the 15th-ranked side on Saturday night.
But none of Australia's established stars could find the match-winner from 19 shots at goal to world No.28 Mexico's 12 in front of 23,167 fans.
It was the Matildas' first game on home soil since their 1-0 Asian Cup final loss to Japan in March, having pulled off a clean sweep of their FIFA Series matches against Malawi and Kenya in April.
Montemurro's review of Saturday's defeat was simple: "We didn't score goals.
"The attacking third - I've said it many, many times - it's so difficult to work, to coach because it's feeling, it's the moment.
"There are many, many things that happen in those areas and the decisions were wrong. It's as simple as that."
The last time Australia played Mexico, the Matildas nabbed a 2-0 friendly win in the US.
Two years on Mexico took their chances when it mattered most.
The visitors nearly drew first blood early in the second half when Matildas star Carpenter - wearing the captain's armband in her 100th match - cheaply gave away possession in the corridor.
Mexican winger Angelique Saldivar broke from the pack and showed her quality by outpacing Australia's defensive trio of Catley, Kaitlyn Torpey and Wini Heatley.
To the relief of the home side, 19-year-old Saldivar missed her target and sent the ball wide of the right post.
But Australia had looked lethal from the outset, starving Mexico of the ball in the opening 15 minutes.
"It's some of the best football we've played in a long, long time," Montemurro said.
"You saw how high the line was. You saw how high Steph was and Wini was. We're trying to actually really dominate games a lot higher.
"It's not in our DNA. We have to still progress and learn that.
"We regained the ball a lot when we lost it, but sometimes the right decision wasn't made. That's probably where we got caught today."
Caitlin Foord was the source of Australia's best first-half chance, keeping her feet as she pushed through Mexican opponents Reyna Reyes and Nancy Antonio to reach Sam Kerr.
Kerr set up Amy Sayer in the 30th minute, but the ball hit the post before Kerr was ruled offside.
Mexico matched Australia's five first-half shots at goal and beat the home side with two on target to none.
A defender with Boston Legacy FC in the NWSL, Nicolette Hernandez was a threat with her left boot and forced a save out of goalkeeper Mackenzie Arnold in the 14th minute, before setting up a flurry of chances.
Australia, having secured direct qualification to the 2027 World Cup after finishing as Asian Cup runners-up, face Mexico again at Parramatta's CommBank Stadium on Tuesday.
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