Whyte completed a protracted take-over of the Scottish champions on 6 May when he acquired Sir David Murray's 85 per cent shareholding.
The deal involved wiping out the club's debt of around 20 million and a pledge of 25m over five years to invest in the squad.
However, just hours after the takeover was completed, Rangers board members released a statement to express doubts about Whyte's cash pledges.
Former board members Alastair Johnston, who headed the independent board committee to review takeover offers, and Paul Murray, both publicly voiced their scepticism - with Murray launching a rival plan.
Once the takeover was completed, both Johnston and Murray were removed from their positions, however, and Whyte believes they should have walked sooner for the benefit of the club.
"I think it's a pity that some of these guys didn't go gracefully instead of going disgracefully," he told Scotland on Sunday.
"Alastair Johnston had a chance to stand down and refused. And so did Paul Murray. It was unfortunate for them. I really don't know what their problem is. Why didn't they resign? It's what any reasonable person would have done."
He added: "The statement (immediately after the takeover] didn't help. It was very difficult to work with the people who were behind that statement.
"It was the most bizarre thing. You couldn't make it up. I don't know, but I hear that some of the previous directors are still sniping away in the background, still trying to cause trouble where they can."
Whyte also revealed that he did not expect suspended directors Martin Bain and Donald McIntyre to be re-instated, as they await the results of an internal inquiry. Asked if there was a chance for them to return, he replied: "No, there's not, no."
Whyte's immediate concerns have not just focused on internal matters, with Rangers under investigation from the HM Revenue and Customs over a tax issue which relates to offshore payments to players from 2001.
The new owner has stated that he is confident of winning the case, however he warned it may linger over the club for years.
"The tribunal only starts in November, so it will likely be concluded around March time," he said.
"Of course, there will probably be a series of appeals after that. This could go on for years yet. If we lose, we appeal and that's another year.
"If we win, HMRC could appeal, so it's not necessarily going away any time soon. It would be nice if it could go away sooner but it will run for some time yet."
In another Sunday newspaper interview, Whyte warned First Minister Alex Salmond to be "very careful" over the way new anti-hate laws are enforced.
He has also insisted that Rangers fans are not "singled out" for special treatment when the new legislation comes into force in time for the new football season, which starts next month.Whyte's remarks come just two months after Rangers were fined 70,000 for sectarian singing by supporters at two Uefa Cup matches against Dutch club PSV Eindhoven.
Uefa found that fans had been guilty of unacceptable chanting both in Holland and at Ibrox. Supporters are also banned from Rangers' first away game in the Champions League next season.
Any repeat in the next three years could see even heavier sanctions imposed by European football's rulers, including a ban on home fans attending games at Ibrox.
Whyte said he was ready to work with Salmond to implement the changes but stressed to the First Minister that such laws should be imposed "equally".
He said: "I don't think we have a problem with sectarian singing at Ibrox. We know the areas we need to address in terms of where it has been creeping back in and that's what we'll do.
"Everyone understands what is acceptable and what is not. I have already had a meeting with Alex Salmond. What I said to him was that I am fully behind what he, the Government and the Scottish authorities are trying to do, and I fully realise we at Rangers have a responsibility to play our part.
"There is no place for sectarian singing at our club, let me be absolutely clear on that, and I believe 99.9 per cent of supporters are of that mindset as well.
"But I did say to him that I did not want to see Rangers fans being singled out in any new legislation.
"The authorities are going to have to be very careful about how they enforce this, and it has to be across the board."
Legislation going through the Scottish Parliament will introduce maximum five-year prison sentences for anyone inciting religious, racial or homophobic hatred through songs, chants and banners.