Steve Clarke's side knew victory would guarantee a place in the knockout stages of a major tournament for the first time, but they were rocked after just 70 seconds.
Grant Hanley was caught out and Ismael Saibari took advantage with a clinical strike into the top corner. He almost made it two as the Scots struggled to find their composure in the Boston Stadium.
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John McGinn appealed for a penalty not long after the restart after being brought down by Neil El Aynaoui, but it was deemed a fair challenge.
Scotland should have been level just after the hour, but Ryan Christie blazed the ball over the crossbar after a brilliant set up from Scott McTominay.
There was more penalty controversy when the Napoli midfielder went down under another dubious challenge from El Aynaou. But, again, the appeals were waved away.
"I don't think it's a penalty," said Sky Sports' Roy Keane on ITV. "I think he's looking to go down."
McTominay and Lyndon Dykes went close late on, but Scotland ended the match with no shots on target.
They need to take something against Brazil on June 24 to have any chance of progression.
VOTE: Should Scotland have had a penalty... or two?
The key moments from Boston...
2: GOAL! Brilliant finish from Saibari gives Morocco the lead.
10: CLOSE! Saibari inches away from tapping home for two.
35: BIG CHANCE! Saibari releases El Khannouss into the box, but it's a wild finish off target.
45+1: FIRST CHANCE SCOTLAND! Patterson's ball misses everyone and McGinn meets it on the volley but sends it high and wide.
49: PENALTY? McGinn brought down by El Aynaoui. The referee deems it a fair challenge.
64: CHANCE! Christie has space to strike from 20 yards but fires over.
82: PENALTY? McTominay brought down by El Aynaoiu, but penalty appeals waved away.
85: CHANCE! McTominay and Dykes go close.
88: CHANCE! McGinn gets a shot away but Riad is there to make a great challenge.
Analysis: Penalty blow, but did Scotland do enough?
It was a nightmare start for Scotland and they took too long to recover from it.
That early blow meant plan A was ripped up and for the rest of the first half it didn't appear that Scotland actually had a plan B.
Once they settled, the chances did come and moments in the second half offered some encouragement ahead of their final Group C match against Brazil.
One, maybe two claims for a penalty and the debate, especially around the challenge on McTominay, will continue.
Yes, we can blame decisions for the defeat but Scotland didn't manage one shot on target.
It was points over performance against Haiti, more was needed against Morocco.
Scotland's dream isn't over but a huge improvement and a fast start will be needed in Miami.
What the result means...
Clarke: Scotland 'ready to go again'
Scotland head coach Steve Clarke speaking to BBC Scotland:
"I thought we were good. Terrible start but the reaction to that was good. We had to dig in for five or 10 minutes just to get our feet in the game.
"Once we were in the game, we showed we could cause them problems. The disappointment would be that we didn't create the one clear-cut chance that would have got us the point.
"This group of players, this squad, have shown that [resilience] in abundance over the years. They're in there, their flat, disappointed, but we've got another chance.
"Everybody is talking about the Scott McTominay [penalty incident]. I actually looked at the John McGinn one, which was 50-50. Some referees would give it, some don't. Sometimes VAR will get involved.
"This team are ready to go again. We're here to try and do what no Scottish team has done before. We gave it everything tonight, and we'll try and do it again."
Christie: Scotland will bounce back
Scotland midfielder Ryan Christie speaking to BBC Scotland:
"Had we played another five minutes, we might just have had them.
"It's frustrating. The start to the game wasn't exactly how we planned it. It would have been easy to chase the game and get a bit disjointed. But we limited them to very little second half and started to play our football.
"It just wasn't to be.
"I've thought the one on McGinn could have been a penalty, I had a good view of that. There wasn't many fouls getting given out there, to be honest.
"We need to take confidence. The immediate feeling is frustration and disappointment. This group of boys will bounce back, we're so together.