Bidding to bounce back from a 6-0 humiliation at Manchester City last weekend, Spurs twice went ahead at White Hart Lane, through Kyle Walker and Sandro, only for Wayne Rooney to hit back on each occasion for United.
Villas-Boas had been strongly criticised in the aftermath of the defeat at City, and although he was satisfied with the improvement in his side's performance, he was angry with the nature of the criticism.
Asked if he felt he had been shown sufficient respect by the media, he told a post-game press conference: "No, I don't think so.
"A couple of people insult my integrity, my human values, my professionalism -- one of these people is sitting over here -- and insults the success that I have achieved in other clubs.
"I don't think it's fair. I think it's a lack of respect and an attack on a person's integrity." Challenged to explain his reservations by the journalist to whom he was referring, Villas-Boas replied: "You can easily understand. I don't need to explain.
"You have always chased people, you attack people. You don't attack them by the front, you attack them sitting when you write.
"You attack integrities, you attack competence, you attack the integrity of a person, their human values, and you don't even know that person.
"You never got a chance to sit down to speak about it. Only when I give you that chance, and I know you and you know me, are you able to reach the conclusions like the ones that you did."
The draw left Spurs in ninth place in the Premier League table, a point behind United and 10 points adrift of leaders Arsenal.
United manager David Moyes conceded that his side had squandered an opportunity to make up ground on the teams above them, but he backed his team to close the gap in the months ahead.
"We're concerned that we're not as close as we'd like to be, but it's a long season," he said. "I think we've still got room to progress and get better, that's undoubtedly. Hopefully we'll be there or thereabouts.
"There's a long way to go, a lot of games coming up in the coming months, the next eight weeks, and we hope to be in the mix at the end of that period."
He also praised the rejuvenated Rooney, who has now scored 10 goals in all competitions this season.
The England striker cancelled out Walker's opener with a close-range finish and then replied to Sandro's 20-yard thunderbolt with a 57th-minute penalty after Spurs goalkeeper Hugo Lloris had felled Danny Welbeck.
"He played well again," said the Scot. "He deserves the adulation he's getting because he's playing well, scoring goals; when the moments come, taking them; and he was very good again today."