It will be "mathematically impossible" for the US and its allies to move all Afghan personnel and families out by August 31, the EU's foreign policy chief Josep Borrell said.
He said that "we have complained" to the Americans that their security at Kabul airport was too strict and it frustrated attempts by Afghans who worked for the Europeans to gain entry.
August 31 is the US deadline for the complete pullout of its forces from Afghanistan, but President Joe Biden suggested that might be extended if airlifts remain viable.
The US military is in control of Kabul's airport and is running its air traffic control operations.
"As far as I know, for the moment the Americans haven't said they will stay beyond August 31, but they might change their thinking," Mr Borrell said.
"They want to evacuate 60,000 people between now and the end of this month. It's mathematically impossible," he said.
Mr Borrell told AFP that, for Europe's evacuation efforts, "the problem is access to the airport – the US checks and security measures are very strong" and were preventing Afghan staff from entering.
He said Brussels lodged a complaint with the US, asking for greater flexibility.
Mr Borrell was in Madrid accompanying European Council President Charles Michel and European Commission President Ursula von der Leyen on a visit to a Spanish air base that received flights carrying European citizens, Afghan personnel, and several American citizens.
He said 150 of the 400 Afghans employed by the EU have been moved out so far. "I'm very aware that this is very insufficient," he said.
"Planes are leaving while people are still on the tarmac," he said.
Despite his exasperation, Mr Borrell denied there were tensions between the EU and the US over the evacuation of Afghanistan.
But, he said, questions will have to be asked about "why things happened like this" and suggested an EU summit may be called to address the situation that Europe has found itself in, and what the next steps should be regarding Afghanistan.
Mr Borrell, who this week told the European Parliament that the chaotic evacuation scenes were a "catastrophe" for the West, underlined that the EU has been working on for some time on a strategy paper that will propose a 50,000-strong rapid reaction force to tackle crises.