The Magpies made the worst possible start to the 2013/14 campaign on Monday, with a dismal showing at the Etihad Stadium, which saw them end the game with 10 men, coming on the back of an unwelcome offer from Arsenal for influential midfielder Yohan Cabaye.
Gutierrez acknowledges that Newcastle fans have every right to be 'angry' with the players just one game into the new season, but has vowed that those inside the St James' Park camp will do all they can to ensure that they bounce back stronger from an early setback.
The Argentine midfielder told the Chronicle: "The fans are going to be angry with us. We have to apologise to them for the result. Yet we must try to give them the points next week.
"We have to take three points in each of the two home games (against West Ham United and Fulham). We have to be strong."
On the City display, he added: "We had to be focused for the 90 minutes. We conceded too quickly and when you do that away from home, it is so hard to come back.
"Then we had the sending off of Steven (Taylor), which did not help us. Maybe Steven's incident was just a yellow. But there's nothing we can do about it now. When you play with 10, though, it is hard for you."
A forgettable night for Gutierrez in Manchester was compounded when he picked up a knock shortly before half-time, with a hamstring complaint proving to be difficult to shake.
He added on his fitness: "It is the same injury as before.
"Now I will go back and try to make the best recovery for the next couple of weeks."