Despite taking four points from their opening two games, England's performances in a 1-0 win over Serbia and 1-1 draw with Denmark have been fiercely criticised for failing to deliver on their tag as pre-tournament favourites.
"We've always known we are one of the team who can win the tournament," Southgate told reporters at his pre-match press conference.
"We haven't changed our objectives. We know to do that, we have to show a different level to what we have so far."
Slovenia have drawn their opening two games and realistically need to take something from the match in Cologne to have any chance of reaching the last 16.
England's Declan Rice said his team are wary of the threat posed by Slovenia striker Benjamin Sesko, who had been linked with a move to join the midfielder at Arsenal, before recently extending his contract with German club RB Leipzig.
"I have watched Slovenia and they have been really good, they have strong players who are really fast. The main talking point is Sesko - he's been a massive target for clubs round Europe," said Rice.
"They are going to come at us and try to win and shock the world."
