"Tottenham are a very good side, our lot worked exceptionally hard," said Gregory, who saw Lee Morris score just before half time to secure the points.
"I'm absolutely delighted for everyone at the club," he added.
"It's been a traumatic month or so and to get a positive result and a clean sheet was very pleasing.
"Losing becomes a habit and you start looking for excuses. There are no excuses, you're in the position you're in because we've not been playing well enough, but we can improve and we will get better."
Gregory praised the fans and the atmosphere at Pride Park adding: "It was like a cup tie. We have to play every game like it's a cup tie and it was really like that in the ground today.
"I'm exceptionally proud of the way they played."
John Gregory was delighted with Derby's 1-0 victory in his first game in charge at Pride Park.