The Portuguese came under pressure following a 6-0 loss at Manchester City last month, and saw Tottenham humbled at White Hart Lane on Sunday.
However, Villas-Boas still believes his team, who sit seventh in the Premier League, can turn things around.
"I won't resign and I'm not a quitter," he said. "This result is difficult for everybody, and they (the fans) suffer much more than us.
"This is a top-four squad, but in the Premier League form isn't there. We have the squad, we believe in each other but the results aren't there to prove it.
"We've worked to build a strong team and we are happy with the signings. The players we have are top quality.
"There is still time to get back on track."
Tottenham trail leaders Arsenal by eight points and have managed less than a goal a game in the top flight this season.
