Rose made his comeback from a three-month injury lay-off in Thursday's 4-1 win over Anzhi Makhachkala.
As Tottenham do not have an abundance of cover at left-back, Villas-Boas shifted Jan Vertonghen out into that position during Rose's absence - a move which did not go down too well with the Belgian, who prefers to play centre-half.
That has led to suggestions that Villas-Boas could make a move for another left-back in the January transfer window.
After spending the majority of the last five seasons out on loan, Rose wants to make the position his own now at Tottenham and he feels has to prove to the manager that he does not need to recruit another body in January.
"That is my job (to persuade Villas-Boas signing another left-back is not necessary)," Rose said.
"And I would be the first one to find out if the club were looking to do that.
"I thought the club were going to do that in August, I went to see the manager, I sat down with him and he told me it was not true and if the club was going to do that he would come and speak to me first hand."
Villas-Boas challenged Rose to secure his position as first-choice left-back in the summer following a successful loan spell at Sunderland.
Rose, 23, grew frustrated with life under Harry Redknapp. He felt he did not get a fair chance under the former Tottenham boss, but he has nothing but praise for the man who replaced him.
"I have a lot of respect for the manager and he has got a lot of respect for me," Rose added.
"He treats me as one of the big players here and it's the first time I have had that at this club."
Rose gave Villas-Boas no reason to seek a new left-back at the start of the campaign as the Englishman slotted in nicely to the starting XI following the departure of Benoit Assou-Ekotto.
Rose's season then hit an abrupt halt following a bizarre injury during Spurs' home win over Tromso in September.
A Tromso player stood on the defender's foot deep inside the away half. Initially it seemed only a minor injury, but Rose ended up needing specialist treatment and was out for almost three months.
"At first thought I had broken my foot but I had torn something underneath it," he said.
"I had a lot of bone bruising but we couldn't see the bone bruising until the swelling had gone down.
"I did my foot against Tbilisi and we were trying to get fit for the Chelsea game, which was about 10 days afterwards, and I have made it even worse trying to get fit for that game.
"It set me back a long time. The manager tried everything he could to get me fit.
"He flew me out to Portugal to see a doctor out there and I did some rehab out there.
"It has been very frustrating. I have missed some important games.
"It has been quite hard to watch at times, especially with it being such a soft injury that I have had. I am just glad I am back now. There are a lot of games coming up and I hope I can stay fit."
With Vertonghen now out until the new year because of an ankle injury, Villas-Boas only has right-back Kyle Naughton and the untested Zeki Fryers as cover if Rose breaks down again.
Rose will not demand a place in the team for Sunday's game against Liverpool, however, as he does not want to suffer a relapse.
"I am not sure (about playing on Sunday)," Rose added.
"No disrespect to Anzhi, but it is totally different to playing a top-class team like Liverpool.
"I wouldn't want to mug myself off and say I could play, and not do myself or the team any justice."
Source: PA
Source: PA