He told Sky News: "We at 4.30 this morning, UK-time, closed the Baron's hotel, shut the processing centre and the gates were closed at Abbey Gate.
"We will process the people that we've brought with us, the 1,000 people approximately in the airfield now and we will seek a way to continue to find a few people in the crowds where we can, but overall the main processing is now closed and we have a matter of hours."
He added: "The sad fact is not every single one will get out."
Mr Wallace also insisted that the Kabul airport terror attack "didn't hasten our departure" and the main UK evacuee processing site was closed "almost exactly on schedule".
"The threat is obviously going to grow the closer we get to leaving," he told Sky News.
"The narrative is always going to be certain groups, such as IS, will want to stake a claim that they have driven out the US or the UK.
"We closed the Baron's hotel almost exactly on schedule. The explosion was horrendous, but it didn't hasten our departure."
Nearly 14,000 British nationals and Afghans were rescued in the mission since the middle of August, Mr Wallace said.
This comes after the Foreign Office defended its Afghanistan embassy staff after documents identifying Afghan workers and job applicants were found left on the ground at the British diplomatic mission in Kabul.