Falcons' stunning 29-20 victory over Gloucester at Kingsholm - their first league away win since February last year - closed the points gap on 11th-placed Wasps.
Newcastle, who have two games left against Saracens and then Wasps, can still avoid the drop after prevailing through tries by flanker Ally Hogg and replacement back-row forward Mark Wilson, while captain Jimmy Gopperth kicked 19 points.
Gloucester wiped out a 19-6 interval deficit to lead by a point with nine minutes left, but Newcastle finished strongly as Wilson's touchdown secured victory and resulted in the home team being booed off.
"From a game-management point of view, we were very good in the first half. We pretty much stuck to plan perfectly, really," South African Gold said.
"We lost our way a little bit in the second half, and if truth be told we got a little bit lucky with our last try, but the character of the players was amazing.
"This is a good bunch of rugby players who are really committed to keeping Premiership rugby in the north-east.
"Our work-rate off the ball was particularly good. The guys really put their hands up today. They don't want to give up, they want to play in the Premiership next season."
Gold, who assumed temporary control in January and will hand over the reins at Kingston Park to Dean Richards next term, admits Newcastle still face a tough task to stay up.
But even if the Falcons finish bottom, their survival hopes will then rest on whether or not this season's eventual Championship winners meet Premiership entry criteria.
"We are in a dire position," Gold added.
"We have been eight points adrift at the bottom of the table and we are playing the Premiership champions (Saracens) next.
"If we start worrying what is going on with other teams and the things we can't control, then we will lose our focus.
"I have always realised the magnitude of this challenge, and it hasn't got any easier. We have always been playing catch-up, but this group of players have really responded well."
Gloucester conjured a try for flanker Akapusi Qera, with fly-half Freddie Burns booting five penalties, but Gloucester's hopes of Heineken Cup qualification next term were severely dented as they even failed to secure a losing bonus point.
Gloucester's top-six ambitions now face a huge examination against Kingsholm visitors Sale Sharks next Saturday following one of their worst home performances in the professional era.
"We looked nervous in the first half, frightened to take the game by the horns and have a real go at it," head coach Bryan Redpath said.
"It is about people taking responsibility and being accountable. With seven minutes to go we had clawed our way back to lead, and then there was another discipline issue. It was bitterly disappointing.
"There are going to be some questions thrown at us, and we must stick together and deal with it, not brush it under the carpet.
"We can't make excuses. We are a good enough side when we want to be, but we are not playing well enough at the moment to see games out and come away with a win. It's about being honest with each other."
Redpath also had no complaints about the fans' booing, adding: "It is hard for the players, but it is also very hard for a group of fans who are very passionate to see us lose in the manner we have lost games this season.
"I can't hide from the fans' frustration. We must accept that, and we can't just shrink into a little corner and hide from it."
And Redpath straight-batted questions about his future, having been linked with taking over at Sale next season.
"There is speculation all the time about who is going where," he said.
"I've got a contract here, and I will fight to do everything I can to make sure we win games. There is no distraction around it."
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