Gutierrez, whose contract expires at the end of the season, was part of the Magpies team which dropped into the Championship after a final-day defeat to Aston Villa in 2009.
Six years on, only victory against West Ham on Sunday will guarantee Premier League football for another year and the 31-year-old is desperate to avoid history repeating itself.
The South American told the Journal: “I don’t have another option than to just think about the game. It’s the most important game I have had to play in seven years.
“The good thing is that we play at home and it’s in our hands. A few players here know what it’s like to go down, and it’s not nice for the city, the players and the club.
“We need move forward to the next game and do it for the fans and the city.”
Gutierrez, who returned to action in March after 18 months out of the game with testicular cancer, admits Sunday’s game at St James’ Park could prove emotional for a variety of reasons, but insists only the club’s fate is important.
“The fans have been really good with me since I arrived, and through my illness. I really appreciated their support,” he added. “I try to do my best for the team and for them. That is more important.”