Roy Hodgson's side need only a point to qualify for the last eight after the 1-1 draw with France and 3-2 win over Sweden.
But Carroll is adamant England will look to end Group D on a positive note.
The Liverpool striker, who scored the opening goal against Sweden, said: "We think we can finish the job against Ukraine. We are confident.
"We showed what we are about against Sweden after going behind and have put ourselves in with a good chance of qualifying. Things are in our hands.
"We will just need a point on Tuesday but we will go there and try and get the win. That's the way we are and approach games."