Spaniard Benitez, more used to challenging for silverware than relegation battles in previous spells in England with Liverpool and Chelsea, faces a tough job, starting with Monday's clash with table-topping Leicester City.
"I have to concentrate on these 10 games," Benitez told reporters on Saturday at his first news conference since being appointed. "I will do my best for us to stay in the Premier League and I am convinced we will.
"I am here because I believe these players are good enough. There are little things that we have to change but we have a good team."
Newcastle are second from bottom with 24 points, one point behind Norwich City who have played two games more and north east rivals Sunderland who have played one more.
After their visit to Leicester they face Sunderland and Norwich in their next two games.
Benitez has never experienced a relegation dogfight in England, but says that will not work against him.
"The responsibility of someone who wants to win a trophy and doesn't want to make a mistake is more or less the same responsibility of someone who doesn't want to make a mistake because you can be relegated," he said.
"I think in terms of approach it's similar."
Benitez, who also managed Valencia, Inter Milan and Real Madrid, said his priority was survival, but said his ambition was to take the club in an upward direction.
"The main thing now is we have 10 games, it doesn't matter if I am the best manager or the worst manager or head coach or whatever, we have 10 games and I have to concentrate on that," he said.
"After these 10 games I think that we will stay in the Premier League, after these 10 games I will be the manager but my first conversation with (managing director) Lee Charnley will be 'what about the future?'
"We hope that we can go in the right direction and be proud of what we are trying to build here."
(Reporting by Martyn Herman, editing by Pritha Sarkar)
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