Owners David Gold and David Sullivan have voiced their support for Grant over the last few weeks despite the club being rooted to the table.
Grant thinks that the pair, who sacked Gianfranco Zola after the Hammers narrowly avoided relegation last year, will stick by him.
"I am being told that they are being patient and understanding," said the 55-year-old.
"We know that this season would be tough. We don't want to be in this situation.
"Today we didn't play well in the second half and we paid for this."