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 told reporters. "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.
|7/2||Tottenham are 7/2 to finish in the top four in 2013-14 with bet365|
"There is still time to get back on track."
Suarez began the rout with an 18th-minute strike, Jordan Henderson and Jon Flanagan also finding the net before the Uruguayan grabbed his second – and 17th of the season – with six minutes to play.
There was still time for Raheem Sterling to add the fifth in the final minute to end a miserable day for Villas-Boas, with Spurs also seeing midfielder Paulinho sent off just after the hour.
"It was difficult for us, Liverpool were spectacular today," he told Sky Sports. "I assume responsibility of the failure; we have to bounce back again.
"In the Premier League things are not going as we expected, as we wanted, so it's normal that frustration is there from everybody.
"It's not me that decides [my future]; I can only work to make things better.
"I don't have to convince anybody [to keep his job], our run is magnificent in the other competitions but not in the Premier League, that is the reality that we face because our slip ups at home haven't allowed us to be in a better position.
"Our ambition to win trophies is still the same; our ambition to qualify for the Champions League is still the same."