The Three Lions came from behind to beat the world's top-ranked side 2-1 in the Nations League clash at Wembley and Southgate was pleased to oversee a victory against elite opposition.
He told Sky Sports: "They're a top side. For sure they caused us problems and we didn't retain the ball well up; we were a bit slow to move it up the pitch.
"But it was a top-level game. We had a lot of young players there, [Declan] Rice, Mount, Trent [Alexander-Arnold], for whom it was a great experience. What pleased me was we had the resilience to see that spell through. Then you get your opportunities and the game starts to open up.
"In the second half, you have to be perfect against these teams without the ball, and bar the one brilliant pass from [Kevin] De Bruyne, we were so compact, our covering positions were good. (Kieran) Trippier was like a soldier out there; unbelievable defensive performance."
Southgate has now challenged England to produce similar performances going forward.
He said: "We've got loads we can get better at. We're not carried away by this win, we've got to back it up against Denmark first and foremost. We know the quality of Belgium today is the level we have to aspire to on a regular basis.
"These are games of concentration and games of detail, and for our guys to come through that was a big moment for them."