England top Group F with 17 points from seven games played and, on Monday, will face the second-placed side, who sit just two points behind.
"It's a great opportunity for us, a home game," Southgate told reporters on Sunday. "We are playing good opposition so we've got to make sure we are tactically prepared, which we will be, but also we've got to have belief in the team that we've got.
"We know the task we have; we know the opportunity. The whole country wants to be at a World Cup. It's a great opportunity for the Wembley crowd to get behind us as well. We have a responsibility to get them on their feet, but equally everywhere we go around the world, the opposition crowds really give the team a lift.
"This result can virtually get us to Russia so everybody wants that and it would be great if we get the level of support that I know that stadium can bring."
Victory on Monday night would take England five points clear at the top of Group F with two games remaining, but should Slovakia win, they will leapfrog the Three Lions into first place.