The Hammers led at the Stadium of Light on two separate occasions but they had to make do with a share of the spoils after Fabio Borini netted a late leveller for Sunderland.
Bilic's team now sit nine points clear of the dropzone, but he has insisted that they still have work to do in order to remain in the top flight.
The 48-year-old is quoted by BBC Sport as saying: "We are disappointed to concede a late goal. It was a fair result. it is a point, we wanted three and we were close.
"They were throwing long balls in, putting the bodies in, from one of those situations they score the goal.
"We have four points from the last two games, we have an unfinished job to do. We have to pick up more points to be safe."
While West Ham sit in 13th position, they are only three points away from moving into the top half of the standings.