The Spurs manager had criticised the "negativity" from supporters following their Premier League win over the Tigers on Sunday, but feels the atmosphere on Wednesday night was key to the club's progression in the competition.
|4/1||Tottenham are 4/1 with William Hill to win the Capital One Cup|
"The atmosphere was excellent because the supporters want to bond with this team, not because of my comments."
It was not all smiles at White Hart Lane, though, as Villas-Boas hinted that absentee Emmanuel Adebayor could face internal punishment after failing to report to the game.
He continued: "Adebayor suffered a setback in training [on Tuesday]. He obviously shows no interest in being here as the players are told to be here [even when not selected]. It's the club rules. This is something for the chairman to deal with."
Veteran keeper Brad Friedel stopped two spot-kicks as Spurs won 8-7 on penalties - the club's first shoot-out win since 1994 - though Villas Boas admitted they had not practiced beforehand.
"We practiced and practiced penalties for the Basel game last year, but we didn't this time," the Portuguese added. "We haven't practiced them for three or four months."
Hull boss Steve Bruce, meanwhile, bemoaned his side's repeated bad luck after taking the lead in extra time only to lose on penalties just days after a controversial penalty call saw them downed 1-0 by Spurs on Sunday.
"I've not really had much luck here in the last couple of days," Bruce said. "But the team showed their resilience and what they're about. I thought we were going to do it when we scored in extra time, but it was not to be.
"It's been a cruel couple of days and especially for Elmo [Ahmed Elmohamady - who was penalised for the match-winning spot-kick on Sunday]. He had a harsh one given against him on Sunday and then he's missed the important one today.
"I've been charged [for my comments following the loss on Sunday]. Mike Riley rang me on Monday morning telling me they've made a huge mistake. What am I supposed to say?
"I thought the referee today was tremendous. We like to see what we've witnessed today and let's not lose that. What is the law and what is it supposed to be? I'll argue my case. It will cost me a few quid, but I'll do it."