Lord Robertson said he is "sad and sickened" by the scenes from the country and to see the Taliban take control of Afghanistan, where coalition forces had been stationed for 20 years.
He served as general secretary of the military alliance between 1999 and 2004 – and personally read out the statement invoking article five of the treaty that provides for collective defence after the attack on the World Trade Centre on 9/11 – said on Monday that the UK should focus on increasing its defences against terrorism at home.
On Sunday, the Taliban marched into Kabul, taking the presidential palace with little resistance, while President Ashraf Ghani was forced to flee.
Lord Robertson said on Good Morning Scotland on Monday that the speed of the takeover showed a "failure of intelligence" from allied forces.
Watch: British personnel arrive in Kabul as Afghanistan crisis unfolds.
"I find it ironic at best but tragic at worst that the anniversary of 9/11 is going to be commemorated in a few weeks' time with the Taliban back in control of Kabul – that is deeply, deeply depressing," he said.
He added that the time for military intervention in the country is over and the focus must shift to stopping terrorist acts on British soil.
"I don't think we're going to be back in there again. We can't go in there militarily – that's over, that's finished.
"That's an episode we'll have to reflect on and learn lots of lessons from.
"But what we have to do is to make sure that our own defences are much more resilient as a consequence of this particular failure, and we've got to watch what the international ramifications are going to be – they will not be good.
"That's why I think it's tragic that we will commemorate the disaster that was 9/11 with the Taliban back in control of the presidential palace in Kabul," he added.
The withdrawal of troops from Afghanistan happened "far too quickly", he said on Monday.
"It didn't have to be like this. If we had learned the lessons of what happened in Bosnia and Kosovo, then a gradual withdrawal based on facts on the ground and success on the ground may have stopped this catastrophe from happening.
"But sadly, we don't learn from the past, we don't learn from previous experiences, and therefore a wholesale withdrawal of American forces meant that the country was left in a condition that has now led to the Taliban taking over."
Watch: Afghanistan – the world watches as Taliban enters Kabul.
The UK should act "swiftly and generously" to aid Afghan citizens who helped UK forces during the two-decade conflict, he added.
Lord Robertson also criticised Foreign Secretary Dominic Raab who was on holiday abroad last week as the Taliban advanced towards the Afghan capital.
"I think it was amazing, staggering, that the Foreign Secretary was still on holiday while Afghanistan was collapsing to the Taliban," he said.
"You've got to be on duty during that sort of period where we are so deeply and intimately involved in it."
The Foreign and Commonwealth Office said Mr Raab had been personally co-ordinating the UK's response and returned to the UK on Sunday.
Looking at the British handling of the war in Afghanistan in the past 20 years, the former NATO secretary-general said: "We bear a big responsibility ourselves.
"We never really took Afghanistan and the conflict there with the seriousness that it demanded.
"We sent people into danger, troops into danger and people died and yet we were not fully, it would appear, committed to the campaign that was going on there.
"I've been critical all along about our country not taking this situation seriously and now the chickens have come home to roost and we're facing a humiliation and a disaster for all of our people."
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Cover image: Personnel from 16 Air Assault Brigade are now on the ground in the Afghan capital of Kabul to assist with the evacuation process (Picture: MOD).