Gonzalo Higuain fired a perfect cross in from the left to Victor Ulloa, who appeared to be fouled by Brad Guzan when after the Atlanta goalkeeper blocked his shot and Ulloa raced up to try again with the rebound.
Guzan, still on the ground, appeared to trip Ulloa with his arms, prompting Miami players to appeal for a penalty call they didn't get.
"That was 100% a penalty,” Inter Miami coach Phil Neville fumed. "Poor refereeing.
"It got reviewed, so whoever reviewed it has let the referee down. We'll put that in the report."
Inter had trailed much of the match after Atlanta's Josef Martinez fired a left-footed shot from the center of the area into the bottom corner to open the scoring in the ninth minute.
Scotland's Morgan finally got the equalizer with a left-footed blast that marked the 2020 Most Valuable Player's first goal of the season.
Neville had challenged Morgan to step things up on attack, and he kept Morgan even though he was cramping late in the second half.
"I didn't want to take him off because I knew you need to keep your match winners, your players on the pitch that can produce moments of brilliance, and he did that," Neville said.
Higuain was back in the lineup and his brother Federico came off the bench in the second half after they missed last week's match against Nashville after the death of their mother.
But Inter were without injured starters Nico Figal and Robbie Robinson and midfielder Blaise Matuidi exited in the 14th minute after colliding with Atlanta's Santiago Sosa.
The match marked a reunion of sorts for Neville and Gabriel Heinze. The two were teammates for one season at Manchester United and Heinze was named head coach of Atlanta shortly before Neville was tapped to lead David Beckham's Inter Miami.
Elsewhere the Seattle Sounders rode second half goals from Raul Ruidiza and super-sub Fredy Moreno to a 2-1 victory over the Portland Timbers in a Cascadia regional clash.
Bill Tuiloma fired in a stunning free kick for the Timbers just before the final whistle, but it was the Sounders who came away with their third victory in four matches this season.
With 10 points they top the Western Conference standings.
After a sedate, scoreless first half, The Timbers had a great chance to take the lead 10 minutes into the second when Jeremy Ebobisse won a penalty kick after Shane O'Neill was whistled for a foul in his own box.
Diego Valeri's first attempt was saved by Sounders keeper Stefan Frei, but he was ruled to have moved off his line too early. Valeri's re-take glanced off the post.
So it was Seattle who opened the scoring from the spot after Timbers keeper Jeff Attinella was called for a foul on Ruidiaz in front of goal.
The Peruvian striker sent Attinella the wrong way and found the net to give seattle a 1-0 lead after 63 minutes.
Montero doubled the score in the 79th with a powerful header off a free kick from Joao Paulo.