The Defence Secretary Ben Wallace has told ITV News ending flights out of Kabul, Afghanistan, on Friday will leave some higher profile people "very worried" and "very scared".
He insisted that Britain had "no choice" but to leave now.
But he admitted that there would be a "few hundred" who hadn't been rescued.
Asked whether he had any regrets, he said: "Every person left behind is a regret".
He said he was proud of what British forces had achieved though, getting 14,000 people out in 14 days.
The practical options for Brits still stuck in Afghanistan are very limited, ITV News' Libby Wiener says
What now for those left behind?The government's plan, it seems, is to keep open the scheme to resettle Afghans who've worked for British forces.But there's little practical assistance the UK can offer them unless they can make their own way to the border.
In the longer run, the defence secretary believes the Taliban will reopen Kabul airport to passenger flights.
'A few hundred' British nationals will be left behind in Afghanistan, but Defence Secretary Ben Wallace thinks there is still hope
Security would be the Taliban's responsibility though, so the idea that their opponents would feel safe venturing to the airport seems somewhat fanciful.
Mr Wallace has made no secret of his opposition to the deal done by US President Donald Trump with the Taliban in Doha last year.
He wouldn't say whether the current operation could have been done differently but implicitly criticised the timetable set by the Americans.
"The whole thing is a personal regret that we had to leave by the 31st August," he said.
Labour leader Sir Keir Starmer said the ending of the evacuation mission in Kabul marks a “sad and dark day” and said the government has “serious questions to answer.
In a statement, he said: “After the despicable acts of violence we witnessed on Thursday, the end of the evacuation from Kabul Airport marks a sad and dark day for many people in Afghanistan.”
He said “with the withdrawal we face the heart-breaking reality that people have been left behind, including many to whom we owe so much”.
“The British government must take its fair share of the responsibility and has serious questions to answer about how, despite having 18 months to prepare, their failure to plan and inability to influence others has contributed to this tragic political failure,” he added.
“We must urgently help the thousands who we have left behind, some of whom are eligible for relocation under the Arap scheme. There are MPs all over the UK who have constituents still pleading for their help.
“The government must work quickly to deliver a strategy to get those people out and work with the UN and partners to quickly deliver essential aid directly to those in need.”