Sunderland were hammered 5-1 at Tottenham on Monday, a result that leaves them at the foot of the table, seven points adrift of safety.
The Wearside club do have games in hand on their relegation rivals, but face Chelsea, Manchester City, Everton and Manchester United - all in the league's top seven - before the season ends.
Manager Poyet conceded after the humbling at White Hart Lane that his side need a "miracle" in order to remain in the top flight, but Cuellar is adamant that Sunderland will keep fighting.
"It is really, really difficult now but we still believe," Cuellar said in quotes reported by the British media.
"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's contract at the Stadium of Light expires at the end of the season, but the defender is keen to extend his stay, regardless of what division Sunderland are in.
"I don't know what will happen next season," he added.
"I would like to be here whatever division we are in but I don't know what is going to happen with me because my contract is finished in the summer.
"My main thing that I am thinking about is to try to keep the club in the Premier League. I am not asking the club what they are doing because the main focus has to be on this season.
"I don't know what is going to happen, but I am really happy at Sunderland and I want to play more games for Sunderland."
