Ahead of their clash with Everton this weekend, West Ham sit two points above the dropzone with five games to play.
Nuno said, "I'm very confident (we will stay up). The performances of the team are giving us all in the Club the hope and the belief and we are competing well.
"There is a lot of football to be played. We have to focus on ourselves and Saturday is a big task for us.
"I focus on the job that I have to do. The game is on Saturday so the stress will come on Saturday! Now is the time to prepare the boys and be focused and live my life not looking further ahead, but day by day!"
Nuno says the Irons support will play a key role tomorrow.
He also said: "It's a tough game against a good team with good players and a good manager in David Moyes, as we all know.
"But it's at London Stadium where we have been improving our own form and have the support of our fans and we count on our fans to help us try and compete well and have a good performance.
"Since we joined, one of our main goals was to try and be comfortable at home and the credit goes to the fans. They realised the situation of the team and really put in the effort to support us and the team is giving back.
"The atmosphere is good and having three of our last five games at home is a positive for us."