The Tigers had performed well in stifling Spurs' attacking threat for much of the game before referee Michael Oliver awarded a penalty to the hosts 10 minutes from time which was duly converted by Roberto Soldado to give Andre Villas-Boas' side a 1-0 victory.
The controversial spot-kick came after Jan Vertonghen's cross was adjudged to have been handled by Ahmed Elmohamady.
"It was very difficult to get in to situations where we could create danger," Villas-Boas said.
"Hull came with one objective which was to prevent us scoring the first goal. We tried hard and were persistent, it was different to the game against West Ham, we kept our cool.
"We played in a very difficult atmosphere, very tense, very negative and we looked like the away team but we kept our cool.
"We had to dig deep within ourselves because we weren't getting help from anybody, the stadium reflected this atmosphere, very tense and without a lot of support until the first goal."
Villas-Boas suggested the negativity played in to the hands of the visiting team but insisted he was not trying to criticise the club's support.
"I'm particularly happy with the way the players fought hard against that anxiety and kept their cool to take the three points," he said.
"I'm extremely happy with the crowd normally, fans for me represent the essence of football. The away support has been immense.
"Sometimes at home it is difficult and it looks like it drags the ball in to our goal rather than our opponent's goal.
"I don't intend with this message to send them a warning, neither do I intend to hurt their feelings but this is something that is felt within the group. It is a feeling that invades us in fixtures like this.
"You need that help. We are great believers in emotion and motivation and that is always decisive when you play at home."
One worry for Villas-Boas would have been an injury to England winger Andros Townsend late in the game.
The 22-year-old ended up with strapping on his wrist after taking a plunge over the advertising hoardings and in to the photographers' pit but Villas-Boas said he expects no lasting damage.