James Cleverly said it was impossible to say how many people were left in Afghanistan who were eligible to come to the UK.
He did not deny thousands of messages were left unread detailing urgent cases of Afghans trying to escape.
Asked if he had unread emails in his inbox, Mr Clevely told the BBC: “I suspect everybody has.
“Obviously we had a limited time window and limited flight availability in Kabul airport. We of course were prioritising getting people who had been processed, who were at the airport, on to planes and out of the country.
“We will continue to work with those Afghans in other parts of Afghanistan who had not been processed when the airport closed and we will continue working to get them out of the country.
“We have been and will continue to work through the significant number of emails that we have received to try to get as many other people out of Afghanistan as possible.”
Whitehall sources have suggested up to 9,000 people who may be eligible to escape have been left behind, such as women and aid workers.
The “vast, vast bulk” of British nationals have left Afghanistan, according to Mr Cleverly.
However, there were also eligible people under the Afghan Relocations and Assistance Policy scheme for people who helped UK forces and others who could be under threat from the Taliban.
“We are going to continue working to get people out who fall into those groups,” he added.
“Predominantly now, of course, it will be in that third group, people at risk of reprisals, whether they be high-profile individuals, of religious minorities or others who may be under severe risk of reprisals from the Taliban.”
As many as 5,000 urgent emails to the Foreign Office with information on Afghans trying to flee Kabul remained unopened, the Observer revealed on Sunday.
Also, Mr Cleverly has defended the organisation’s response to the crisis in Afghanistan after people called for Dominic Raab to be sacked.
He insisted the allegations about the Foreign Secretary’s style of leadership were “not true” and the organisation had responded swiftly to the unprecedented events.
It comes after Mr Raab faced criticism for being on holiday in Crete as the Taliban advanced.
It comes after one government source told The Times, “I think he is toast in the next reshuffle.”
The source added the Foreign Office “is a poorly-led organisation with a control freak in charge who won’t delegate anything”.
But Mr Cleverly told Times Radio: “I don’t know where that’s where that’s coming from. The organisation that I see really sprang quickly into an activity that was at a scale and nature that was unprecedented.”
Asked directly whether Mr Raab was a “control freak”, Mr Cleverly said: “No, that’s not true. It’s not true.”
He added: “It was a brutal, horrible, incredibly difficult time and yet, as I say, we were able to evacuate over 15,000 people and that is a herculean task.”