A 5-1 defeat to Tottenham Hotspur on Monday night left the Black Cats seven points from safety in the Premier League, but Cuellar believes that they must continue to fight in the seven games that are remaining.
"It is really, really difficult for us now but we still believe," the Spaniard told reporters.
"We have too many games to go to give up on survival now.
"We still have teams in the relegation area to play at home and we must take hope from that."
Sunderland host Everton in their next game on Saturday afternoon.