Goals from Carlos Tevez, David Silva, Vincent Kompany and a James Perch own goal consigned the Magpies to a defeat that leaves them just three points clear of relegation, heading into home fixtures against Fulham and Sunderland.
And Gutierrez has stated that there is no excuse for their poor performance against the Premier League holders and emphasised the need to pick up more points.
"No excuses - we have to do better, we were missing important players who had injuries but we have players who can come in to do the job the same way.
"We have to take a few more wins. We are not going to be safe with the points that we have so we need more points. We have two home games which are going to be difficult for us so the next 15 days are the most important of the year."
Gutierrez did make the admission that Manchester City are a strong team, but was adamant that Newcastle should have started better, though he did praise the way they responded at the start of the second half.
"They have good players but we have to play better than we did today," he added. "We know that it's a hard place to come - they're the champions, they have fantastic players, but we have to start the game with a higher ambition, a higher intensity, because if not you have a defeat like today.
"I think after half time, we started playing like we should have started the first half but then I think the third goal killed us.
"But we had to attack them from the beginning, not wait until half time because normally in the Premier League it can be too late."