Asked if the evacuation was evocative of the US departure from Vietnam in 1975, he said: "Let's take a step back. This is manifestly not Saigon."
President Ashraf Ghani confirmed he has left the country, leaving it unclear how power would be transferred following the sweep across Afghanistan that brought the Taliban back to the capital two decades after it was overthrown by US-led forces.
Sources told Reuters that most US staff were expected to be evacuated from Kabul in the coming day or two.
A NATO official said all commercial flights had been suspended and only military aircraft were allowed to operate. The alliance said it was helping to keep the airport running.
France and Germany, members of NATO, said on Sunday they were moving their diplomats to the airport and sending military transport planes to Kabul to evacuate their citizens and their Afghan helpers.
A US intelligence assessment earlier in the week had said Kabul could be encircled in 30 days and could fall to the Taliban within 90 days, but the insurgents captured most of Afghanistan's major cities in less than a week and entered the capital on Sunday.
About 4,200 people remained in the US embassy until Thursday, when the Taliban's rapid gains forced the Biden administration to begin flying in thousands of troops to help pull out many of the remaining diplomats.
The deployment included an additional 1,000 soldiers from the 82nd Airborne Division, who President Joe Biden said on Saturday would help evacuate citizens and ensure an "orderly and safe" drawdown of US military personnel.
On Sunday, US officials said they were weighing whether more troops were needed. Another 3,000 are on standby in Kuwait.
Washington invested billions of dollars over four US administrations in Afghan government forces, giving them advantages over the Taliban, but they were unable to defend the country in the face of the militants' advance, Blinken told CNN.
The United States' original mission in Afghanistan, launched to oust al Qaeda chief Osama bin Laden after the Sep 11, 2001, attacks, had been fulfilled, Blinken said, saying Washington had prevented further attacks by militants harboured by the Taliban.
But Biden has faced rising domestic criticism after sticking to the plan to withdraw, which was agreed under his Republican predecessor Donald Trump. On Saturday, Biden defended his decision, saying an "endless American presence in the middle of another country's civil conflict was not acceptable to me".
Republican lawmaker Michael McCaul said a Taliban takeover would revive the threat to the United States.
"We are going to go back to a pre-9/11 state. A breeding ground for terrorism," he told CNN on Sunday.
Biden met with his national security team on Sunday by secure videoconference from the presidential retreat at Camp David to hear updates on evacuations and the security situation, a White House official said.
US Senate Majority Leader Chuck Schumer, a Democrat like Biden, said at a news conference that the safety of US personnel and of Afghans who supported the Americans should be Washington's top concern.
"Job number one is for us to bring back, first, all American personnel ... But second, all of the brave Afghans who helped our military, they have to be provided an exit to come to America," Schumer said.