Sunderland boss Gus Poyet conceded after Monday's 5-1 defeat at Tottenham Hotspur that his side will likely need 'a miracle' in order to avoid relegation.
Poyet's team remain bottom of the Premier League table, seven points from safety with seven games to play.
Cuellar admits Sunderland have it all to do if they are to preserve their top-flight status, but has called on those at the Stadium of Light to keep the faith - with fixtures against fellow strugglers Cardiff City, West Bromwich Albion and Swansea City still to come.
He said in The Sun: "It is really, really difficult now but we still believe.
"We have too many games to give up on survival. We have teams down near us still to play and we have to take some hope from that.
"It is too early to say or think we are relegated. We keep fighting.
"We must try and clear our minds of the last few weeks and get back to the performances at the start of the year when we were playing well.
"If we play the same as we did then, we can be okay."
Cuellar, who has spent the last two years at Sunderland, has also revealed that he will be looking to extend his expiring contract in the summer, even if that means turning out in the Sky Bet Championship.
The Spanish defender added: "I would like to be here whatever division we are in.
"But I am not asking the club what they are doing because the main focus has to be on this season."