The city's response to the tragedy is "a very thin silver lining in a very dark cloud", the UK Government minister said.
Mr Carmichael spoke after visiting emergency services at the command centre at the site of Friday night's accident in which a police helicopter landed on the Clutha pub in Glasgow.
He then met with Glasgow City Council leader Gordon Matheson and signed a book of condolence set up in the council's headquarters.
"It's a very thin silver lining in a very dark cloud, but I think the response of the community in Glasgow has been absolutely magnificent," Mr Carmichael said.
"Adversity often brings out the best in people. I don't think there are any communities in the world that would respond in the way Glasgow has responded and is responding."
Mr Carmichael, wearing a badge that said "People Make Glasgow", said the slogan "summed up the response you saw late on Friday night into the early hours of Sunday morning".
He said: "Glasgow is no stranger to tragedy, we have seen it over the years. But the response of the people of the city I think has spoken volumes about the strength of the community and its courage and character."
People would want answers about the cause of the crash but the investigations may take some time.
"Time spent now taking care in the investigation will pay dividends at a later stage," he said, adding that he has "every confidence" that both the Air Accidents Investigation Branch and police will fulfil their roles "completely professionally".
But the Orkney and Shetland MP said his experience both as a solicitor and "as a Member of Parliament who has had helicopter tragedies take place in my own constituency in Shetland" show that such investigations are complicated and take time.
"The natural instinct of people who are grieving is to want to know how they lost their loved one. I would say though your best chance of knowing that is if as much evidence is gathered from the scene now which can then be evaluated and investigated and assessed at a later stage," he said.
"If it is possible for information to be shared with families as the investigation progresses then I hope it will be, but at the same time there would be no purpose served by putting ill-considered conclusions out into the public domain. You can see how that could end up causing even more pain to the grieving. Informed answers are what we need."
He told how he learned of the crash when civil servants texted him on Friday night. Since then he has been in contact with UK Transport Secretary Patrick McLoughlin and with the Prime Minister's office, saying: "The Prime Minister has made it very clear that if any assistance, either at strategic or operational level, is required by Police Scotland, that can be provided by a police force south of the border then they will have it."
Shadow Scottish secretary Margaret Curran accompanied Mr Carmichael during the visit to the command centre and to the council.
Ms Curran, who represents Glasgow East, said "there is a real sense of shock" in the city and stressed the need to "pull together as a city and keep the city together as we face the tragedy and try to support those who have lost their loved ones, support their families and make sure the services are working well".
She said: "I'm a Glasgow MP. I'm a Glaswegian. The city has been amazing. This is Glasgow where, in the deepest tragedy, we rally to support each other. But it is hard times and the city is hurting. We have to move on, move on to asking some of the questions about why this happened and what we do now."
Scottish Labour deputy leader Anas Sarwar, MP for Glasgow Central, also signed the book of condolence.
"It's been a sad few days but although we've seen the most tragic of scenes, we have also seen the best of our citizens, the way the people of Glasgow have come together, with passers-by coming to support the emergency services who were so brave in getting the situation under control, putting their own lives on the line as they did so," he said.
"A time will come when people will want to know more detail about what happened, but I think it's right in the short term we focus on making sure we're giving people the support they need."
A silent queue formed at Glasgow City Chambers as members of the public came to sign the book of condolence.
Among them was Kevin Lynch, 39, from Airdrie, a trainer with a charity which helps young people into training and employment.
"We have some of the young people with us, and they wanted to come down here and pay their respects. Everybody has been coming in this morning feeling rather sombre, rather down and depressed.
"We talked amongst ourselves, my colleagues and I, and we felt it was it was fitting we pay our respects, both as an organisation and ourselves as well."
Another one who came to sign the book was 17-year-old Levi McDonald from Rutherglen.
"I just wanted to pay my respects for the loved ones of the victims," he said.