Drogba has been much criticised for his poor form this season, and Scolari questioned his commitment shortly before his dismissal last week.
He has also been linked with a move to Italy to rejoin his former manager Jose Mourinho at Internazionale, but Drogba insisted he wants to stay.
"I am happy with everyone here and want to be a Chelsea player," Drogba told reporters.
"I want people to stop talking about me going back to Marseille or going to Inter Milan. When Jose Mourinho left I was unhappy but that is past now and I am allowed to change my mind. I want to stay until the end of my contract.
"I love the fans. My family love it here and we want to stay. There have been no talks about extending my deal but there is time for that.
"I would stay if they offered me a new deal. I know that first I need to show I am still the Didier Drogba this club knows."
That seemed a direct rebuttal of Scolari's comments, which clearly stung the 30-year-old striker.
"When Scolari started blaming individuals, then that was bad. To name one player as to blame for what happened in a squad of 24 is wrong," Drogba said.
"I was shocked he said that. How can one player be responsible for not winning for so many weeks and losing points?”
"This is not an individual sport. When you win games everyone is happy and enjoys it together. But when we lose we have to lose together too.
"And if I had as much power with the owner as has been said, then Mourinho would still be here, no? If I had that power!”
"I have respect for Scolari as a man and a coach but I was not involved in any discussions with the owner."