The Blacks Cats have been specialists of the great escape in recent seasons, but their current position is their most perilous yet as they sit bottom of the table and nine points from safety with only six games of the season remaining.
Sunderland are winless in their last eight matches too, although they did end a seven-match goal drought against the Hammers before Fabio Borini's 91st-minute equaliser rescued a point.
"Honestly, that's as positive as I've felt after a game for a long time," Cattermole told reporters.
"If we have to start with a draw, we'll start with a draw, but I think you'll definitely see us look to build on that. We will behind the scenes."
Sunderland's next match sees them face fellow strugglers Middlesbrough on April 26.