Spurs' season has been littered with spectacular performances as they also won 3-0 at Manchester United, beat Aston Villa 4-1 and dumped City out of the League Cup.
But they lost 2-1 at home to Ipswich before the international break and were also defeated at Crystal Palace and Brighton.
James Maddison celebrated his 28th birthday with a double before Pedro Porro and Brennan Johnson also got on the scoresheet, condemning City to a fifth straight defeat in all competitions.
The win lifts Spurs to sixth place in the Premier League table, three points behind fourth-placed Arsenal.
"It is significant because obviously they've got an unbelievable record here at home," said Postecoglou.
"So I don't think it's something that (we) can be just sort of blase about. It is significant, but I think it's significant for the whole group.
"We've reached these standards before. It's about now not dropping as we have in certain games."
Maddison had been dropped for the past two league games but made a huge impact on his return to the starting line-up.
The midfielder had also missed out on a call-up to the England squad and Postecoglou said he had harnessed that free time over the past two weeks to get back to his best.
"I could just sense that he was ready for a big game," added the former Australia boss.
"He hasn't sort of lowered his ambitions or his kind of levels, the kind of player he wants to be. It's about us giving him that platform.
"It wasn't just his goals today. I thought he was important for us in the build-up because he was always looking for tight areas. Defensively, he worked really hard.
"I still think he's had a decent season, but it's like us as a team. We want to be more than that. We want to be more than just a decent team."
