In her first game of the day, Gauff teamed up with world number six Jessica Pegula to face Czech Republic duo Karolina Muchova and Linda Noskova.
After taking the first set, Gauff and Pegula were unable to continue their momentum, falling to a 6-2 4-6 5-10 defeat.
The American pairing started strongly and raced into an early lead, taking the opening set in what seemingly looked like a straightforward victory for Team USA.
However, Muchova and Noskova rallied and in a second set that saw five break points converted by both, the Czech's would prevail to take the game to a decider.
Gauff and Pegula lost four straight games to put their opponents in the ascendency, with Muchova and Noskova able to see out the win to progress to the quarter-finals.
Gauff emerged back onto the clay courts in the French capital for her mixed-doubles match soon after, joining Taylor Fritz to face a Canadian pairing of Felix Auger-Aliassime and Gabriela Dabrowski.
The American duo would come from a set down to take the game to a decider, but it would be their opponents who emerge 6-7 (2-7) 6-3 8-10 victors.
Gauff and Fritz exchanged blows with the Canadians, but were edged out in a first set tie-break after losing four games on the spin.
But not wanting to let their dreams of a medal die, the American pair would recover from losing an early break point to rally and earn one of their own in the eighth game, seeing out the win to take Gauff to her second third-set decider of the day.
However, the same result would transpire, with Auger-Aliassime and Dabrowski edging a nail-biting conclusion to book their place in the quarter-finals of the competition.
Murray's final tournament ended in the quarter-finals at Roland-Garros as he and Dan Evans were beaten in straight sets by American duo Tommy Paul and Taylor Fritz.
The 37-year-old left Court Suzanne-Lenglen to a standing ovation as the curtain came down on a career that included three Grand Slam titles, as well as singles gold at both the London and Rio Games.
"I feel good. I have been ready for this moment for the last few months since I had the operation on my back," said Murray.
"I knew it was the right time and I feel lucky to come and compete here.
"I am grateful to Dan (Evans) for putting in the effort he did to give us a good chance of having a great run. I am looking forward to stopping now."
While Murray and Evans had pulled off miraculous comebacks against Japan’s Kei Nishikori and Taro Daniel and Belgium's Sander Gille and Joran Vliegen in the previous rounds, both Paul and Fritz proved to be a step too far.
The British pair were second best for much of the contest, despite showing signs of yet another comeback in the second set only for Fritz's strong service game to cinch victory for the Americans.
"I mean it was a great run and we lost to two top players today. They are both top tennis players, we would have had to play very well to win that match and we didn’t.
"We got into it at the end, but if we found that form earlier we could have caused them problems, but it wasn't to be.
"We did make the quarters, but if you get through that match you get an opportunity to win a medal."
Murray bows out having won 739 of his 1001 ATP Tour level matches, earning 46 singles titles across his career as well as spending 41 weeks as world number one.
But in true Murray fashion, he posted to X joking he never liked the sport he played for 18 years shortly after the defeat.
The two-time gold medallist had twice come from the jaws of defeat at the tournament, but there was to be no miracle this time as they were beaten 6-2 6-4 in the quarter-finals.
Murray and Evans endured a nightmare start to proceedings, conceding a double break to their American opponents which proved to be decisive in deciding the opening set.
Despite a better start in the second, Paul and Fritz would again stamp their authority on the encounter, racing into a 5-2 lead and to within a game of victory.
But as shown in the previous rounds, Murray and Evans showcased grit and determination to claw themselves to within a game of levelling the contest after saving one match point in the eighth game.
However, Fritz's strong serving would come to the fore as it had done throughout the contest on Court Suzanne Lenglen, making no mistake to wrap up the victory.
Paul and Fritz will face Matthew Ebden and John Peers for a place in the final, potentially setting up an all-American clash with Austin Krajicek and Rajeev Ram.
Data Debrief: Murray's farewell ends in disappointment
There was to be no comeback from Murray and Evans this time around, as tennis says goodbye to one of its greatest ever players.
But the encounter belonged to the Americans, whose performances on serve proved to be the difference at Roland-Garros.
Fritz and Paul would win 63% of their 40 first serve points, winning seven service games compared to the Brits' four.
Musetti, who was beaten by Novak Djokovic in the semi-finals, prevailed 6-4 1-6 6-3 on Saturday at Roland-Garros.
It marked a historic success for Italy, bringing up the nation's first tennis player to win a medal at the Olympics since Uberto de Morpugo in 1924, with those Games having also taken place in Paris.
While Auger-Aliassime leaves empty-handed from the singles, he did win bronze in the mixed doubles.
Prior to Musetti's triumph, Tommy Paul and Taylor Fritz won in straight sets to claim the bronze medal in the men's doubles, beating Tomas Machac and Adam Pavlasek.
After falling to defeat to eventual gold medallists Matthew Ebden and John Peers in the semi-finals, the American duo dusted themselves down to claim a 6-3 6-4 victory.
Paul and Fritz controlled the opening set, earning a double break in the sixth game and, despite losing the next two, held on to take the early advantage.
The Americans squandered three match points to seal the win, but confirmed their place on the podium in the 10th game, with Team USA taking home two medals from the doubles after Austin Krajicek and Rajeev Ram's silver earlier in the day.
It was not all doom and gloom for Czechia, though, with Machac and Katerina Siniakova having claimed gold in the mixed doubles on Friday.
Murray's glittering career came to an end on Thursday in the Olympics men’s double quarter-finals as he and Dan Evans were beaten in straight sets by American pair Tommy Paul and Taylor Fritz.
He announced before the Games that it would be the final tournament of his career, and he pulled off two superb comeback wins, saving multiple match points in both, to make it to the last eight.
Murray bows out as a two-time Olympic gold medallist with three grand slams. He won 739 games across his 1001 ATP Tour level matches, winning 46 singles titles.
Five of those came at Queen's Club, and shortly after his retirement was confirmed, the newly named Andy Murray Arena was announced.
"Andy is the greatest tennis player ever to come from this country and a giant of British sport," LTA chief executive Scott Lloyd said in a statement.
"His contribution to the game is immense and has bought us all so many moments of pride. He was relentless in his pursuit of excellence and had a single-minded determination to succeed.
"We are proud to name the arena at our tournament at the Queen's Club after him."
Meanwhile, Novak Djokovic has led the tributes to Murray, having played him 36 times over the course of their careers.
"Andy, we were all hoping that this message will never come, but here it is," Djokovic said in a message uploaded to the ATP Tour's X account.
"I just want to say congratulations for an amazing career, multiple grand slams, number one in the world, two Olympic gold medals, a Davis Cup. You've done it all. Amazing, really.
"Congratulations to you, to your family. We go back a long time. I think we were 11 when we met the first time on the court, and we had some incredible encounters, and rivalries.
"We played finals of every single grand slam. You brought the Wimbledon title to Britain after 77 years, unfortunately, against me in the final, but it was quite a special historic moment that I cherish and was grateful to be part of.
"You can be proud of your incredible resilience and fighting spirit, the inspiration that you give to all of us after all the hardships you went through - the surgery, the restrictions in your movement.
"You still kept going, you showed everyone there is no letting go and no giving up. Kudos to you and all the best to you and your family. You deserve the best possible farewell."
Zverev slipped during his third-round triumph against Cameron Norrie in SW19, bowing out of the competition in a five-set to Taylor Fritz in the following round.
The world number four has since competed in the Hamburg Open, a title he won a year ago, but fell at the final hurdle to Arthur Fils in a decisive final set tie-break.
Zverev, who became the first German to win an Olympic gold medal in singles since Steffi Graf did so in 1988, beat Karen Khachanov in the final in Tokyo four years ago.
The German described his injury as a bone edema and torn capsule and said that it did not require surgery ahead of the games.
"To be honest, you know, the risk will stay for the next two, three, four weeks maybe because that's how long the bone heals, and that's what everybody told me," Zverev said.
"But, at the end of the day I also knew that I don't want to rest for four weeks because, now we're playing on the surface where I don't see that big of a risk of doing the same motion again and doing the same movement again."
The tennis will take place at Roland Garros, a venue well-known to Zverev who reached the French Open final earlier this year, losing out on a first grand slam title to Carlos Alcaraz in five sets.
Zverev is also on the shortlist of German athletes who could be flagbearer for the nation during Friday's opening ceremony.
"If someone told me that I should walk in as a flag bearer, it would mean even more to me, to be honest (than winning the Olympics)," Zverev was quoted by SpilXperten.
"Leading an entire nation and so many top German athletes into the Olympics is simply the greatest honour an athlete can receive.
"And of course, the gold medal I won at the last Olympics is one of the highest achievements you can have in sports and for me personally the greatest success in my career."
