The England international started Tuesday’s 3-1 defeat to Napoli on the bench, but was forced into action during the first half after Jose Bosingwa pulled up with a hamstring problem.
Thirty-one-year-old Cole has reportedly told Villas-Boas that he believes the Blues won’t win any trophies because of the 34-year-old’s tactics.
However, when quizzed about any confrontation with the former Arsenal defender, the young Portuguese manager replied: "It's not true.
"You don't expect them to be jumping up and down with excitement when the manager doesn't use them," the former Porto coach said when asked whether the players backed him.
"The club is more important than any individual. Full backing, part backing or whatever backing - it doesn't matter."
Midfielder Frank Lampard is another who appeared unhappy after being forced to start the loss in Italy on the bench.
While admitting the England international found the decision to watch from the beginning hard to take, Villas-Boas insists Lampard accepted his decision.
"In the end it is the decision of the manager and Frank accepts that," added the Blues' manager.
"Of course it is difficult for him. It is a difficult decision to take, but it is always taken in the best interests of the team.
"Sometimes whatever you say to players is not enough to convince them your choice is the right one.
"I don't have any regrets about team selection. It was what I felt was completely right. The team was well set up."
