During a dramatic day of racing on Tuesday, Archibald, 27, had been looking to repeat the gold medal success she managed as part of the same team event in Rio de Janeiro five years ago.
However, although the Great Britain quartet broke the previous world record in their semi-final and bettered it in the final, it was still not enough to deny Germany a stunning gold medal.
"I think that was the big fight for the day, try and make it into the gold medal final then you're guaranteed an Olympic medal," Archibald said.
"That was something special to get on the start line and say we've won something here."
Archibald and fellow Scot Neah Evans had earlier survived a scare after the two riders crashed into one another as they slowed down after beating the United States in the semis, although both were quickly back up.
Archibald said she was "utterly mortified" about the crash.
Speaking to former Tour de France winner Bradley Wiggins in an interview after the bizarre incident, Archibald said: "I think that's going to be the last thing I think about on my deathbed.
"I couldn't have gone into a better person, Neah was so understanding and we went into the final with nothing to lose.”
Archibald's wasn't the only crash involving a Team GB cyclist in the velodrome on Tuesday.
In the men's team pursuit, rookie Harry Tanfield was crashed into by Denmark's Frederik Madsen, a collision that prompted a furious reaction from the Dane, even though it was his own fault.
Great Britain’s cycling squad members have established a formidable reputation for excellence, with Archibald managing to reach peak physical condition for the Tokyo games despite major disruption to her normal training routines in the build-up as a result of the coronavirus pandemic.
During an incredible cycling career, Archibald has amassed 50 medals at Olympic and Commonwealth Games, World and European Championships and UCI Track World Cup meetings.