Alderweireld headed home an 80th-minute corner as Spurs came from behind to earn local supremacy and move above their neighbours in the pursuit of European football.
A hard-fought 2-1 win was a vast improvement from Spurs' meek showing at Bournemouth when they failed to register a single shot on target in a forgettable 0-0 draw.
"Of course [Bournemouth] hurt," Alderweireld told Standard Sport. "There was some negativity about us in the media - that's normal but nobody sees how hard we're working to change things.
"I don't want to say, 'No, all the criticism, everything [people say] is untrue' but of course it hurts because we work so hard. Everyone wants to change things, everyone wants better results.
"Sometimes you just need some momentum and confidence. I think from minute one [against Arsenal], after a couple of seconds, we had a shot on goal. That showed what our intentions were."
Arsenal broke the deadlock against the run of play after 16 minutes when Alexandre Lacazette capitalised on Serge Aurier's loose touch to fire into the top corner from 25 yards.
But Spurs hit back within three minutes when Sead Kolasinac's wayward back-pass left David Luiz wrong-footed and Heung-min Son pounced to score his first goal since the restart.
Jose Mourinho criticised his side's mental strength after the defeat at Sheffield United but Alderweireld says they showed their resilience and believes it could prove a turning point under the Portuguese.
"Even after a very good goal from them, mentally we were strong and we came back quickly," the centre-half said. "At difficult moments we stood our ground, especially defensively, and we have the quality to change it.
"I think after the lockdown defensively we've been a lot stronger. We're getting there. We have some momentum going, so I think last night can be a changing point. In this period when things aren't 100 percent going your way, the thing is to work very hard and it'll come. Last night we showed we have character. At difficult moments we were there. And then we have quality [to score]."
Spurs leapfrogged Arsenal into eighth - which will not be enough for a Europa League place after Manchester City's European ban was lifted this morning.
"Every season we try to finish above them," said Arsenal goalkeeper Emiliano Martinez. "We need to make sure we finish above them. I feel sorry for the supporters because we know what it means for them.
"Our target is Europe, that is the reality. We are going to try and give our best against Liverpool [on Wednesday] and reach the FA Cup Final."