The 20-year-old flyweight lost 20-10 to Cuba's Robeisy Ramirez Carrazana at the Excel Arena in London on Friday.
His defeat came after fellow Team Ireland fighter Paddy Barnes was narrowly defeated in his light-flyweight bout with China's Zou Shiming.
Conlan slipped three points behind in the first round as his opponent went on the front foot to open up a 6-3 lead.
The gutsy Irish sixth seed was closer in the second but lost it by a score of 4-3.
In the final round the Cuban unleashed a flurry of punches on Conlan after he turned his back, forcing him to take a standing count.
It finished 10-4 and with a final score of 20-10 the west Belfast fighter will come home with a bronze medal at his first Olympics.
The disappointed Irishman said afterwards he lost to a better boxer on the night.
"He was the best fighter of the night," said Conlan.
We have amazing support back home, all great fans, so I'm sorry for letting them down but you'll see me in the future and I'll be a lot better.
"His defence was great, he was a better man than me. He didn't punch that hard but he was just sharp in his attacks.
"I was wasting a lot of energy throwing punches. I should have been waiting for my time but I was a bit eager tonight going for a gold medal."
Watching the fight back in Belfast were Michael's friends and his younger brother Sean Paul.
"We're very proud of him," he told UTV. "He boxed his best and that's the best anyone's going to do against that Cuban, everyone's delighted for him.
"He's done everyone proud and he's still coming home with a medal - as long as he's won one fight in the Olympics I'll be happy!
"It's amazing for him and Paddy to get a medal of any colour."
Earlier, Barnes drew his fight with Zou 15-15 in the ExCeL Arena - but bowed out of the 2012 Games 45-44 on countback as a single point swayed the judges in favour of the three-time world champion and defending Olympic champion.
Barnes trailed 11-8 at the end of the second round, but fought back to draw level at 15-15 by the end of the fight.
He connected with a series of rights and lefts as he went all out to cut the deficit in the third, in what was an impressive display from the Belfast man.
Speaking after the match, he said they were all close rounds.
"I wish he had've beaten me by a couple of points cause it's so, so close, it's even more heartbreaking.
"But I got a bronze. I made history. That's a bit of consolation.
"He's very very illusive and hard to pin down," Barnes said of his opponent. "Once I got the three scores in the first round I knew it was going to be a tough fight."
The 25-year-old said the match was a "nightmare".
He continued: "I was actually dreaming of it this morning, but it's turned out to be a nightmare now.
"[Shiming's] tactics worked in the end. We both got a fair crack of the whip," he reasoned, "it could've gone either way and it's just unfortunate it went his way."
Paddy Barnes' family and friends who were watching the fight back home said they "couldn't be prouder" of him.
His brother Gareth told UTV: "I'm well proud of him.
"You can see on his face the reaction that he was disappointed but then again he will get over it and you can't do much but accept it. I couldn't be prouder of him."
Fellow bronze medal winner Hugh Russell said: "He'll be disappointed of course but it's an enormous achievement - he's coming back with a bronze medal from the Olympic Games and it's not a failure.
"This kid is the only person in boxing history to ever win two Olympic medals at different Games and he has to be proud of that."
Barnes won his quarter-final fight on Wednesday against Indian fighter Devendro Laishram.
He is the first Irish boxer to win two medals in consecutive Olympics Games, following his bronze in Beijing in 2008. Zou had already ended his dream of winning gold four years ago, with a 15-0 crushing win.
When questioned about possibly meeting him in the ring again, Barnes commented: "He's getting old, I wish he was older."
Sports Minister Carál Ní Chuilín has congratulated the Belfast pair.
"Our boxers have once again shone on the global stage - proving to be ambassadors for their sport, their communities and themselves," she said.
"But any sense of disappointment is more than eclipsed by a feeling of pride on what has been achieved today, and every day competitors from the North have taken part in competition.
"I applaud all local athletes across the whole range of sports."
Meanwhile Mullingar's John Joe Nevin will box for Olympic gold after beating Cuban Lazaro Alvarez Estrada in their bantamweight semi-final earlier on Friday.
He will fight Luke Campbell of Britain for the title on Saturday.