The Dutchman, who has no previous experience of either playing or coaching in Italy, was appointed two weeks before the start of the season to replace Roberto Mancini who left the club by mutual consent.
Inter have won four and lost six of their 12 competitive matches in Serie A and the Europa League under his leadership and have slipped to 14th in Serie A.
"I don't know if I will still be here on Wednesday, all I can do is work hard," said De Boer, who is Inter's eighth coach since Jose Mourinho left after winning a Serie A, Coppa Italia and Champions League treble in 2010.
"It's always difficult when you lose three matches in a row but I know that we can improve a lot and we saw that in the second half.
"It's a difficult time for everyone, and for me in particular, but the only thing I can do is to continue to work hard," he added. "I still feel that the club has faith in me."
Inter, enduring their fifth season without Champions League football, were sunk by an 88th-minute penalty converted by Mauricio Pinilla, although Mauro Icardi had a goal disallowed in stoppage time for a foul on Atalanta goalkeeper Etrit Berisha.
"When things are going against you, you don't get any luck with the referees either. I saw from the bench that Icardi did not commit the foul, he was pushed by the Atalanta defender," added De Boer.
"It's always difficult to win here in Bergamo but we gifted them the first half. It wasn't my Inter."
Chinese electronics retailer Suning Commerce Group Co Ltd bought nearly 70 percent of Inter for €270 million in June, less than three years after the club had been sold to a consortium led by Indonesian business tycoon Erick Thohir.
Inter have said that Thohir will remain as president.
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