Southgate's men have also seen off Tunisia and Panama in the group stage, while suffering defeat to Belgium with a second-string side, and the England boss is expecting an increase in quality this evening.
"They'll be the best team we've played in terms of what they're capable of doing with the ball, and what their individuals are capable of, definitely," he told reporters.
"For us as a team, it's another chance to create a small piece of history. We've got to keep getting over those hurdles and I know we talked about the success of the younger teams but this is a much harder, much bigger level for the players and the belief is building as things are happening.
"The more of these tests we can come through, the better, not just for now, but moving forward."
England have met Croatia once before at a major tournament, winning 4-2 in a group-stage match at Euro 2004.