Sugar questioned Villas-Boas' tactical approach in midweek and even suggested ex-Manchester United manager Sir Alex Ferguson should come out of retirement to replace the Portuguese at White Hart Lane.
"I've struggled to understand AVB's tactics," Sugar told talkSPORT in the wake of Spurs' 6-0 defeat at Manchester City last Sunday.
"The formation that AVB plays, I don't understand at all. I put my hands up, I am no great football expert, but I don't understand it at all.
"My dream would be that my good friend Sir Alex Ferguson will get itchy feet in about a year or so and decide he wants to get back into management and maybe bring his wonderful wife down to London and manage our team."
But after a fighting draw with David Moyes' United side Villas-Boas hit back.
"I think it's a very driven agenda by somebody that doesn't honour the club, neither myself nor my players," Villas-Boas told BBC Radio 5Live.
"It's their team, their passion and they don't trade it for anything else, not like Alan Sugar who trades it for money."
Villas-Boas, who saw his side twice give away the lead against the reigning Barclays Premier League champions, was also in prickly mood when he spoke to the written press.
The former Chelsea boss said he was feeling disrespected before becoming embroiled in a heated exchange with a reporter after taking exception to a piece written earlier in the week.
"A couple of people insult my integrity, my human values, my professionalism and one of these people is sitting over here," he said.
"It insults the success that I have achieved in other clubs and I don't think it's fair. I think it's a lack of respect and an attack on a person's integrity.
"I don't want to undermine other managers. You can easily compare situations. We have sat above Man City before and above Man United before and we haven't seen any kind of these personal attacks to somebody so I think that is unfair.
"It's something that obviously comes with the 6-0 thrashing but more important is the team and the response and I think the players did that in great, great fashion."
Kyle Walker scored his first Tottenham goal in over 19 months as he opened the scoring with a low free-kick before the England defender then failed to clear a Phil Jones cross and allowed Wayne Rooney to level.
Sandro then scored a wonderful effort to put the hosts back in front, with Rooney equalising from the penalty spot shortly afterwards.
Villas-Boas felt his side had done enough to win the game but was pleased with the reaction following last weekend's thrashing.
"A very good first and second half," he said of his side's performance.
"We had great chances to go 2-0 up in the first half.
"So I think we deserved something. It was a good response to the heavy defeat that we took at Man City. Not perfect because perfect would have been to win the game but a good response from a group of players that want to do well. It keeps us in touch with the group at the top and gives us the motivation to go forward."
Moyes was disappointed that his players could not carry over their midweek Champions League form, which saw them hammer Bayer Leverkusen 5-0 in Germany, and was left bemoaning just two points from United's last two league outings.
"We had a great win in midweek," he said.
"But for a minute in Cardiff near the end you would have been saying that Man United had a really good week. It is not easy place to come, Tottenham.
"They had their own pride which they showed in their performance. So it was disappointing. United have to win. That was why in the end we were trying to get a third goal but we could not quite do it."